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[34] Underfull \vbox (badness 1708) has occurred while \output is active [35] [36] [37] Overfull \hbox (0.42216pt too wide) detected at line 1597 \OML/cmm/m/it/10.95 T \OT1/cmr/m/n/10.95 : \U/msb/m/n/10.95 R[] \U/matha/m/n/10 .95 Ý[]Ñ \U/msb/m/n/10.95 R[]\OML/cmm/m/it/10.95 ; \U/matha/m/n/10.95 p\OML/cm m/m/it/10.95 x; y\U/matha/m/n/10.95 q ÞÑ p\OML/cmm/m/it/10.95 T[]\U/matha/m/n/1 0.95 p\OML/cmm/m/it/10.95 x; y\U/matha/m/n/10.95 q\OML/cmm/m/it/10.95 ; T[]\U/m atha/m/n/10.95 p\OML/cmm/m/it/10.95 x; y\U/matha/m/n/10.95 qq ^^P [] [38] Overfull \hbox (2.916pt too wide) in paragraph at lines 1717--1718 []\T1/cmr/m/it/10.95 Der Flä-chen-in-halt ei-nes [39] Underfull \vbox (badness 10000) has occurred while \output is active [40] Underfull \vbox (badness 10000) has occurred while \output is active [41] Underfull \vbox (badness 10000) has occurred while \output is active [42] Underfull \vbox (badness 1983) has occurred while \output is active [43] [44] [45] [46] Underfull \vbox (badness 10000) has occurred while \output is active [47] Underfull \hbox (badness 10000) in paragraph at lines 2224--2226 Underfull \vbox (badness 1371) has occurred while \output is active [48] Underfull \vbox (badness 10000) has occurred while \output is active [49] [50] Kapitel 3. 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Da-mit wird $\U/matha/m/n/10.95 p\U/msb/m/n/10.95 D[]\O ML/cmm/m/it/10.95 ; d[]\U/matha/m/n/10.95 q$ \T1/cmr/m/n/10.95 zu ei-nem me-tri -schen Raum, dem \T1/cmr/m/it/10.95 Ein-heits-ballm-odell \T1/cmr/m/n/10.95 der $\OML/cmm/m/it/10.95 n$\T1/cmr/m/n/10.95 -dimensionalen [66] [67] Underfull \vbox (badness 5388) has occurred while \output is active [68] [69] Overfull \hbox (3.34332pt too wide) in paragraph at lines 3211--3213 \T1/cmr/m/n/10.95 das heiÿt $\OML/cmm/m/it/10.95 $ \T1/cmr/m/n/10.95 is län-ge n-treu. 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[36] Underfull \vbox (badness 1708) has occurred while \output is active [37] [38] [39] Overfull \hbox (0.42216pt too wide) detected at line 1597 \OML/cmm/m/it/10.95 T \OT1/cmr/m/n/10.95 : \U/msb/m/n/10.95 R[] \U/matha/m/n/10 .95 Ý[]Ñ \U/msb/m/n/10.95 R[]\OML/cmm/m/it/10.95 ; \U/matha/m/n/10.95 p\OML/cm m/m/it/10.95 x; y\U/matha/m/n/10.95 q ÞÑ p\OML/cmm/m/it/10.95 T[]\U/matha/m/n/1 0.95 p\OML/cmm/m/it/10.95 x; y\U/matha/m/n/10.95 q\OML/cmm/m/it/10.95 ; T[]\U/m atha/m/n/10.95 p\OML/cmm/m/it/10.95 x; y\U/matha/m/n/10.95 qq ^^P [] [40] Overfull \hbox (2.916pt too wide) in paragraph at lines 1717--1718 []\T1/cmr/m/it/10.95 Der Flä-chen-in-halt ei-nes [41] Underfull \vbox (badness 10000) has occurred while \output is active [42] Underfull \vbox (badness 10000) has occurred while \output is active [43] Underfull \vbox (badness 10000) has occurred while \output is active [44] Underfull \vbox (badness 1983) has occurred while \output is active [45] [46] [47] [48] Underfull \vbox (badness 10000) has occurred while \output is active [49] Underfull \hbox (badness 10000) in paragraph at lines 2224--2226 Underfull \vbox (badness 1371) has occurred while \output is active [50] Underfull \vbox (badness 10000) has occurred while \output is active [51] [52] Kapitel 3. [53] [54] [55] Underfull \vbox (badness 10000) has occurred while \output is active [56] [57] [58] [59] [60] [61] [62] Underfull \hbox (badness 10000) in paragraph at lines 2812--2813 Overfull \hbox (2.53337pt too wide) in paragraph at lines 2815--2816 []\T1/cmr/m/it/10.95 Ist $\OT1/cmr/m/n/10.95 ^^A \U/matha/m/n/10.95 „ \U/msb/m/ n/10.95 E[]$ \T1/cmr/m/it/10.95 ein eu-kli-di-sches Overfull \hbox (7.89157pt too wide) in paragraph at lines 2867--2869 []\T1/cmr/m/it/10.95 Ist $\OT1/cmr/m/n/10.95 ^^A \U/matha/m/n/10.95 „ \U/msb/m/ n/10.95 S[]$ \T1/cmr/m/it/10.95 ein sphä- [63] Underfull \hbox (badness 10000) in paragraph at lines 2880--2882 [64] [65] [66] Kapitel 4. Underfull \vbox (badness 10000) has occurred while \output is active [67] Overfull \hbox (5.96252pt too wide) in paragraph at lines 3019--3021 \T1/cmr/m/n/10.95 gilt. Da-mit wird $\U/matha/m/n/10.95 p\U/msb/m/n/10.95 D[]\O ML/cmm/m/it/10.95 ; d[]\U/matha/m/n/10.95 q$ \T1/cmr/m/n/10.95 zu ei-nem me-tri -schen Raum, dem \T1/cmr/m/it/10.95 Ein-heits-ballm-odell \T1/cmr/m/n/10.95 der $\OML/cmm/m/it/10.95 n$\T1/cmr/m/n/10.95 -dimensionalen [68] [69] Underfull \vbox (badness 5388) has occurred while \output is active [70] [71] Overfull \hbox (3.34332pt too wide) in paragraph at lines 3211--3213 \T1/cmr/m/n/10.95 das heiÿt $\OML/cmm/m/it/10.95 $ \T1/cmr/m/n/10.95 is län-ge n-treu. 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Ein $\U/matha/m/n/10.95 p\OML/cmm/m/it/10.95 ^^U; ^^O\U/ matha/m/n/10.95 q$\T1/cmr/m/n/10.95 -quasi-geodätisches [90] [91] Underfull \vbox (badness 10000) has occurred while \output is active [92] Underfull \vbox (badness 1048) has occurred while \output is active [93] Underfull \vbox (badness 10000) has occurred while \output is active [94] [95] Underfull \vbox (badness 1478) has occurred while \output is active [96] Overfull \hbox (5.06831pt too wide) in paragraph at lines 4392--4393 []\T1/cmr/m/n/10.95 Eine wich-ti-ge Be-ob-ach-tung: Je-der me-tri-sche Raum $\U /matha/m/n/10.95 p\OML/cmm/m/it/10.95 X; d\U/matha/m/n/10.95 q$\T1/cmr/m/n/10.9 5 , der quasi-isometrisch zu $\U/matha/m/n/10.95 p[]p\OML/cmm/m/it/10.95 G; S\U /matha/m/n/10.95 q\OML/cmm/m/it/10.95 ; d[]\U/matha/m/n/10.95 q$ [97] Underfull \vbox (badness 2343) has occurred while \output is active [98] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd) [99] [100] Kapitel A. 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[7] LaTeX Font Warning: Font shape `U/stmry/b/n' undefined (Font) using `U/stmry/m/n' instead on input line 314. [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 790. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 790. [20] [21] [22] Underfull \vbox (badness 4217) has occurred while \output is active [23] [24] Kapitel 2. [25] [26] Overfull \hbox (7.47366pt too wide) in paragraph at lines 1098--1099 []$\U/matha/m/n/10.95 p\OML/cmm/m/it/10.95 M; d\U/matha/m/n/10.95 q$ \T1/cmr/m/ n/10.95 heiÿt $\OT1/cmr/m/n/10.95 2$\T1/cmr/m/it/10.95 -Punkt-homogen\T1/cmr/m/ n/10.95 , falls es für je zwei Punk-te-paa-re $\U/matha/m/n/10.95 p\OML/cmm/m/i t/10.95 p[]; p[]\U/matha/m/n/10.95 q\OML/cmm/m/it/10.95 ; \U/matha/m/n/10.95 p\ OML/cmm/m/it/10.95 q[]; q[]\U/matha/m/n/10.95 q$ \T1/cmr/m/n/10.95 mit $\OML/cm m/m/it/10.95 d\U/matha/m/n/10.95 p\OML/cmm/m/it/10.95 p[]; p[]\U/matha/m/n/10.9 5 q ^^P Underfull \vbox (badness 1024) has occurred while \output is active [27] [28] [29] [30] [31] [32] Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 1351. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `superscript' on input line 1351. 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[36] Underfull \vbox (badness 1708) has occurred while \output is active [37] [38] [39] Overfull \hbox (0.42216pt too wide) detected at line 1597 \OML/cmm/m/it/10.95 T \OT1/cmr/m/n/10.95 : \U/msb/m/n/10.95 R[] \U/matha/m/n/10 .95 Ý[]Ñ \U/msb/m/n/10.95 R[]\OML/cmm/m/it/10.95 ; \U/matha/m/n/10.95 p\OML/cm m/m/it/10.95 x; y\U/matha/m/n/10.95 q ÞÑ p\OML/cmm/m/it/10.95 T[]\U/matha/m/n/1 0.95 p\OML/cmm/m/it/10.95 x; y\U/matha/m/n/10.95 q\OML/cmm/m/it/10.95 ; T[]\U/m atha/m/n/10.95 p\OML/cmm/m/it/10.95 x; y\U/matha/m/n/10.95 qq ^^P [] [40] Overfull \hbox (2.916pt too wide) in paragraph at lines 1717--1718 []\T1/cmr/m/it/10.95 Der Flä-chen-in-halt ei-nes [41] Underfull \vbox (badness 10000) has occurred while \output is active [42] Underfull \vbox (badness 10000) has occurred while \output is active [43] Underfull \vbox (badness 10000) has occurred while \output is active [44] Underfull \vbox (badness 1983) has occurred while \output is active [45] [46] [47] [48] Underfull \vbox (badness 10000) has occurred while \output is active [49] Underfull \hbox (badness 10000) in paragraph at lines 2224--2226 Underfull \vbox (badness 1371) has occurred while \output is active [50] Underfull \vbox (badness 10000) has occurred while \output is active [51] [52] Kapitel 3. [53] [54] [55] Underfull \vbox (badness 10000) has occurred while \output is active [56] [57] [58] [59] [60] [61] [62] Underfull \hbox (badness 10000) in paragraph at lines 2812--2813 Overfull \hbox (2.53337pt too wide) in paragraph at lines 2815--2816 []\T1/cmr/m/it/10.95 Ist $\OT1/cmr/m/n/10.95 ^^A \U/matha/m/n/10.95 „ \U/msb/m/ n/10.95 E[]$ \T1/cmr/m/it/10.95 ein eu-kli-di-sches Overfull \hbox (7.89157pt too wide) in paragraph at lines 2867--2869 []\T1/cmr/m/it/10.95 Ist $\OT1/cmr/m/n/10.95 ^^A \U/matha/m/n/10.95 „ \U/msb/m/ n/10.95 S[]$ \T1/cmr/m/it/10.95 ein sphä- [63] Underfull \hbox (badness 10000) in paragraph at lines 2880--2882 [64] [65] [66] Kapitel 4. Underfull \vbox (badness 10000) has occurred while \output is active [67] Overfull \hbox (5.96252pt too wide) in paragraph at lines 3019--3021 \T1/cmr/m/n/10.95 gilt. Da-mit wird $\U/matha/m/n/10.95 p\U/msb/m/n/10.95 D[]\O ML/cmm/m/it/10.95 ; d[]\U/matha/m/n/10.95 q$ \T1/cmr/m/n/10.95 zu ei-nem me-tri -schen Raum, dem \T1/cmr/m/it/10.95 Ein-heits-ballm-odell \T1/cmr/m/n/10.95 der $\OML/cmm/m/it/10.95 n$\T1/cmr/m/n/10.95 -dimensionalen [68] [69] Underfull \vbox (badness 5388) has occurred while \output is active [70] [71] Overfull \hbox (3.34332pt too wide) in paragraph at lines 3211--3213 \T1/cmr/m/n/10.95 das heiÿt $\OML/cmm/m/it/10.95 $ \T1/cmr/m/n/10.95 is län-ge n-treu. Dar-aus folgt mit den De-fi-ni-tio-nen der Me-tri-ken be-reits $\OML/cm m/m/it/10.95 d[]\U/matha/m/n/10.95 p\OML/cmm/m/it/10.95 \U/matha/m/n/10.95 p\O ML/cmm/m/it/10.95 p\U/matha/m/n/10.95 q\OML/cmm/m/it/10.95 ; \U/matha/m/n/10.9 5 p\OML/cmm/m/it/10.95 q\U/matha/m/n/10.95 qq ^^P Underfull \vbox (badness 10000) has occurred while \output is active [72] Underfull \vbox (badness 10000) has occurred while \output is active [73] Underfull \vbox (badness 5578) has occurred while \output is active [74] [75] [76] [77] Underfull \vbox (badness 1824) has occurred while \output is active [78] Underfull \vbox (badness 10000) has occurred while \output is active [79] [80] [81] [82] Kapitel 5. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 3639. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `\delta' on input line 3639. Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref) removing `math shift' on input line 3639. [83] Underfull \vbox (badness 10000) has occurred while \output is active [84] Overfull \hbox (6.92796pt too wide) in paragraph at lines 3746--3747 []\T1/cmr/m/n/10.95 Die klas-si-schen hy-per-bo-li-schen Räu-me $\U/matha/m/n/1 0.95 p\U/msb/m/n/10.95 H[]\OML/cmm/m/it/10.95 ; d[]\U/matha/m/n/10.95 q$\T1/cmr /m/n/10.95 , $\U/matha/m/n/10.95 p\U/msb/m/n/10.95 L[]\OML/cmm/m/it/10.95 ; d[] \U/matha/m/n/10.95 q$ \T1/cmr/m/n/10.95 und $\U/matha/m/n/10.95 p\U/msb/m/n/10. 95 D[]\OML/cmm/m/it/10.95 ; d[]\U/matha/m/n/10.95 q$ \T1/cmr/m/n/10.95 sind $\O ML/cmm/m/it/10.95 ^^N$\T1/cmr/m/n/10.95 -hyperbolisch [85] [86] Overfull \hbox (17.33647pt too wide) in paragraph at lines 3821--3823 \T1/cmr/m/n/10.95 für al-le $\OML/cmm/m/it/10.95 x; y \U/matha/m/n/10.95 P \OML /cmm/m/it/10.95 X$\T1/cmr/m/n/10.95 . Ins-be-son-de-re sind $\U/matha/m/n/10.95 p\OML/cmm/m/it/10.95 ^^U; \OT1/cmr/m/n/10.95 0\U/matha/m/n/10.95 q$\T1/cmr/m/n /10.95 -quasi-isometrische Ein-bet-tun-gen ge-ra-de $\OML/cmm/m/it/10.95 ^^U$\T 1/cmr/m/n/10.95 -Bilipschitz- [87] [88] Underfull \vbox (badness 10000) has occurred while \output is active [89] Overfull \hbox (12.37329pt too wide) in paragraph at lines 3971--3972 []\T1/cmr/m/n/10.95 Bevor wir die Aus-sa-ge be-wei-sen, lei-ten wir die wich-ti g-ste Fol-ge-rung her. Ein $\U/matha/m/n/10.95 p\OML/cmm/m/it/10.95 ^^U; ^^O\U/ matha/m/n/10.95 q$\T1/cmr/m/n/10.95 -quasi-geodätisches [90] [91] Underfull \vbox (badness 10000) has occurred while \output is active [92] Underfull \vbox (badness 1048) has occurred while \output is active [93] Underfull \vbox (badness 10000) has occurred while \output is active [94] [95] Underfull \vbox (badness 1478) has occurred while \output is active [96] Overfull \hbox (5.06831pt too wide) in paragraph at lines 4392--4393 []\T1/cmr/m/n/10.95 Eine wich-ti-ge Be-ob-ach-tung: Je-der me-tri-sche Raum $\U /matha/m/n/10.95 p\OML/cmm/m/it/10.95 X; d\U/matha/m/n/10.95 q$\T1/cmr/m/n/10.9 5 , der quasi-isometrisch zu $\U/matha/m/n/10.95 p[]p\OML/cmm/m/it/10.95 G; S\U /matha/m/n/10.95 q\OML/cmm/m/it/10.95 ; d[]\U/matha/m/n/10.95 q$ [97] Underfull \vbox (badness 2343) has occurred while \output is active [98] (/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd) [99] [100] Kapitel A. Underfull \hbox (badness 10000) in paragraph at lines 4574--4575 [101] [102] Kapitel B. 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LaTeX Font Warning: Some font shapes were not available, defaults substituted. ) (see the transcript file for additional information)pdfTeX warning (dest): name {vierfuenfdrei} has been referenced but does not exist, replaced by a fixed one {/usr/share/texmf/fonts/enc/dvips/cm-super/cm-super-t1.enc} Output written on HyperGeo.pdf (163 pages, 940314 bytes). Transcript written on HyperGeo.log. Result: ExitSuccess Running /usr/bin/convert -verbose HyperGeo.pdf[0] -resize 70x HyperGeo.png in an env with 4 entries: "gs" -q -dQUIET -dSAFER -dBATCH -dNOPAUSE -dNOPROMPT -dMaxBitmap=500000000 -dAlignToPixels=0 -dGridFitTT=2 "-sDEVICE=pngalpha" -dTextAlphaBits=4 -dGraphicsAlphaBits=4 "-r72x72" -dFirstPage=1 -dLastPage=1 "-sOutputFile=/tmp/magick-um2HwSm8-%08d" "-f/tmp/magick-uNhemguw" "-f/tmp/magick-Fd38GMBU" /tmp/magick-um2HwSm8-00000001 PNG 595x842 595x842+0+0 8-bit DirectClass 14.6KB 0.010u 0:00.019 HyperGeo.pdf[0]=>HyperGeo.pdf PDF 595x842 595x842+0+0 16-bit DirectClass 14.6KB 0.000u 0:00.000 HyperGeo.pdf[0]=>HyperGeo.png PDF 595x842=>70x99 70x99+0+0 16-bit DirectClass 0.040u 0:00.019 Result: ExitSuccess Running /usr/bin/optipng -verbose HyperGeo.png in an env with 4 entries: OptiPNG 0.6.4: Advanced PNG optimizer. Copyright (C) 2001-2010 Cosmin Truta. ** Processing: HyperGeo.png 70x99 pixels, 2x16 bits/pixel, grayscale+alpha Input IDAT size = 1662 bytes Input file size = 1957 bytes Trying: zc = 9 zm = 8 zs = 0 f = 0 IDAT too big zc = 9 zm = 8 zs = 1 f = 0 IDAT size = 1633 zc = 1 zm = 8 zs = 2 f = 0 IDAT too big zc = 9 zm = 8 zs = 3 f = 0 IDAT too big zc = 9 zm = 8 zs = 0 f = 5 IDAT too big zc = 9 zm = 8 zs = 1 f = 5 IDAT size = 1591 zc = 1 zm = 8 zs = 2 f = 5 IDAT too big zc = 9 zm = 8 zs = 3 f = 5 IDAT too big Selecting parameters: zc = 9 zm = 8 zs = 1 f = 5 IDAT size = 1591 Output IDAT size = 1591 bytes (71 bytes decrease) Output file size = 1886 bytes (71 bytes = 3.63% decrease) ** Status report 1 file(s) have been processed. Result: ExitSuccess