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Sur l'effondrement à l'infini des variétés asymptotiquement plates.

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(1)Sur l’effondrement à l’infini des variétés asymptotiquement plates. Vincent Minerbe. To cite this version: Vincent Minerbe. Sur l’effondrement à l’infini des variétés asymptotiquement plates.. Mathématiques [math]. Université de Nantes, 2007. Français. �tel-00195953�. HAL Id: tel-00195953 https://tel.archives-ouvertes.fr/tel-00195953 Submitted on 11 Dec 2007. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(76) æµÿF济ß8‹ô &‡|浊ßõà:ˆŽß8‡F浊ßõà‡|8‹ñ “8‹‘#‘#ñ²ŒEõ8‰9æ o‡|8‹57à’8‹ñŽŒ&ò ŒŠÿŽß89à’à’8õãÔô@济ã “5 8 Ž + Š5 75Š˜8‹‘ õ8‡ñ’济ßæµ5ö@8‹ñŽ + Š576‹öیŽŠ‘’6óõ8E

(77) æµÿ|济ß8‹ôԎßæ

(78) ‰ ŒŽß8&8‹52ã578Š576‹öیŽŠ‘’6óö>ŽßæµÿuŒŽß8>D  ‘²Œ5ۑõæµ5576rã5‡|浊5ۑ o u57æµã7à ‰9æµ57à#Šßõ6‹ñ’8‹ñ’æµ57àõ89à‡|浊ßõàò]ŒŠßಌ5ˆ‘Š5ˆ‘’8‹ñ#ô@8‹5ŠñŽŒoò]æµ57‰‹‘#Šßæµ5 õŠßà#‘²Œ57‰98&ö@69æˆõ69à#Šßêˆã78 r = d(o, Œã ‡|浊5ۑ o 7ŒŠ57à#Š%êˆã78ŽŒEò]æµ57‰‹‘#Šßæµ5 .) o. ρo : t 7→. tn . vol B(o, t). $52‡|8‹ã‘ñ’8½Œñ’êÛã78‹ñêÛã78‰98‹‘#‘’8 ò]æµ57‰‹‘#Šßæµ5 ρ Œ‡‡uŒñ²Œ7:ߑõ7Œ57àƒŽß8 ‘#é769æµñ“8&õ8BŠßà#é7浇û(*ñ’æ “æ ô åډ®ò#D‘#é769æµñ “8b<D < D ë3:8‹ŽŽß8.89à#‘‰‹ñ’浊ßà’ಌ5ۑ’o8.êˆãuŒ57õŽŒd‰9æµãñ#ÿãñ’83õ8.ƒŠß‰9‰‹Š 89à#‘Ô‡Fæ>à#Š‘#Šô@8>D%8 ñ’69à#㎐‘²Œ‘à#㊐ôµŒ5ˆ‘89à#‘ã5 ‡|浊5ۑ‰‹Žß6õ8&‰98‹‘#‘’8‘#!é 9à’8>D ó—C™7¨)â Fš =D =D <

(79) F³µ¹Ú± M n  n ≥ 3  ´

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(84) ‡F浑#!é 9à’8  ν å @ë vol B(o, t) t ∀ t ≥ s > 0, ≥C r¯¶l¸º´ˆ­ . M. M. 2n n−2. 2. vol B(o, s). Š o‡ŽŠßêˆã78ŽŒ o  Š57æµñ²Œ‘#Šßæµ5. o. 2 n−2. s. ∀ t ≥ 1, vol B(o, t) ≥ Co vol B(o, 1)tν. å +ˆë. 8‹‘õ69‰9æµãŽß8óõ8Ž +,8‹57‰ Œµõñ’8“8‹5ۑ. ∃Ao , Bo > 0, ∀t ≥ 1, Ao tν ≤ vol B(o, t) ≤ Bo tν .. . å ë.

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(93) «óÙ  ´

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(95) |³µ¹± M n  n ≥ 4  ´

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(100) F³µ¹Ú± M n  n ≥ 4  ´

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