alpha brooks Book Archive

Geometry And Topology

Actes de la Table ronde de geometrie differentielle: En by Arthur L. Besse (Ed.)

By Arthur L. Besse (Ed.)

Résumé :
En juillet 1992, une desk Ronde de Géométrie Différentielle s'est tenue au CIRM de Luminy en l'honneur de Marcel Berger. Les conférences qui sont reproduites dans ces Actes recouvrent l. a. plupart des sujets abordés par Marcel Berger en Géométrie Différentielle et plus précisément : l'holonomie (Bryant), los angeles courbure [courbure sectionnelle confident (Grove), courbure sectionnelle négative (Abresch et Schroeder, Ballmann et Ledrappier), courbure de Ricci négative (Lohkamp), courbure scalaire (Delanoë, Hebey et Vaugon), courbure totale (Shioya)], le spectre du laplacien (Anné, Colin de Verdière, Matheus, Pesce), les inégalités isopérimétriques et les systoles (Calabi, Carron, Gromov), ainsi que quelques sujets annexes [espaces d'Alexandrov (Shiohama et Tanaka, Yamaguchi), elastica (Koiso), géométrie sous-riemannienne (Valère et Pelletier)]. Les auteurs sont pour los angeles plupart des géomètres confirmés, dont plusieurs ont travaillé avec Marcel Berger, mais aussi quelques jeunes. Plusieurs articles (Bryant, Colin, Grove...) contiennent une présentation synthétique des résultats récents dans le domaine concerné, pour mieux les rendre obtainable à un public de non-spécialistes.

Proceedings of the around desk in Differential Geometry in honour of Marcel Berger
July 1992, a around desk in Differential Geometry used to be geared up on the CIRM in Luminy (France) in honour of Marcel Berger. In those complaints, contributions disguise lots of the fields studied via Marcel Berger in Differential Geometry, particularly : holonomy (Bryant), curvature [positive sectional curvature (Grove), destructive sectional curvature (Abresch and Schroeder, Ballmann and Ledrappier), adverse Ricci curvature (Lohkamp), scalar curvature (Delanoë, Hebey and Vaugon), overall curvature (Shioya)], spectrum of the Laplacian (Anné, Colin de Verdière, Matheus, Pesce), isoperimetric and isosystolic inequalities (Calabi, Carron, Gromov), including a few similar topics [Alexandrov areas (Shiohama and Tanaka, Yamaguchi), elastica (Koiso), subriemannian geometry (Valère and Pelletier)]. Authors are usually geometers who labored with Marcel Berger at a while, and in addition a few more youthful ones. a few papers (Bryant, Colin, Grove...) contain a short evaluate of modern ends up in their specific fields, with the non-experts in brain.

1. time table of the Mathematical talks given on the around Table

Lundi thirteen juillet 1992

K. GROVE : challenging and smooth sphere theorems
T. YAMAGUCHI : A convergence theorem for Alexandrov spaces
J. LOKHAMP : Curvature h-principles
G. ROBERT : Pinching theorems less than quintessential speculation for curvature

Mardi 14 juillet 1992

Y. COLIN DE VERDIERE : Spectre et topologie
H. PESCE : Isospectral nilmanifolds
F. MATHEUS : Circle packings and conformal approximation
R. MICHEL : From warmth equation to Hamilton-Jacobi equation
C. ANNE : Formes diff´erentielles sur les vari´et´es avec des anses fines
G. CARRON : In´egalit´e isop´erim´etrique de Faber-Krahn

Mercredi 15 juillet 1992

E. CALABI : in the direction of extremal metrics for isosystolic inequality for closed orientable
surfaces with genus > 1
M. GROMOV : Isosystols
Ch. CROKE : Which Riemannian manifolds are decided via their geodesic flows

Jeudi sixteen juillet 1992

R. BRYANT : Classical, extraordinary and unique holonomies : a standing report
T. SHIOYA : habit of maximal geodesics in Riemannian planes
L. VALERE-BOUCHE : Geodesics in subriemannian singular geometry and control
D. GROMOLL : optimistic Ricci curvature : a few contemporary developements
Ph. DELANOE : Ni’s thesis revisited
E. HEBEY : From the Yamabe challenge to the equivariant Yamabe problem
Vendredi 17 juillet 1992
W. BALLMANN : Brownian movement, Harmonic capabilities and Martin boundary
U. ABRESCH : Graph manifolds, ends of negatively curved areas and the hyperbolic
120-cell space
N. KOISO : Elastica
Jerry KAZDAN : Why a few differential equations don't have any solutions
J. P. BOURGUIGNON : challenge session

2. at the contributions

Among the above pointed out meetings, 5 aren't reproduced in those notes,
namely these by means of Christopher CROKE, Detlef GROMOLL, Jerry KAZDAN, Ren´e

Some of them were released in other places, particularly :

Conjugacy and pressure for manifolds with a parallel vector field
J. Differential Geom. 39 (1994), 659-680.
Lp pinching and the geometry of compact Riemannian manifolds
Comment. Math. Helvetici sixty nine (1994), 249-271.
On the opposite hand, Professor SHIOHAMA, who used to be invited to offer a conversation, had
not been capable of come to the desk Ronde. He sought after however to give a
contribution to Marcel Berger. it's been further to this quantity.

Show description

Read or Download Actes de la Table ronde de geometrie differentielle: En l'honneur de Marcel Berger PDF

Best geometry and topology books

Zeta Functions, Topology and Quantum Physics

This quantity specializes in a number of facets of zeta features: a number of zeta values, Ohno’s kinfolk, the Riemann speculation, L-functions, polylogarithms, and their interaction with different disciplines. 11 articles on contemporary advances are written through notable specialists within the above-mentioned fields. every one article starts off with an introductory survey resulting in the interesting new study advancements finished through the members.

Additional info for Actes de la Table ronde de geometrie differentielle: En l'honneur de Marcel Berger

Example text

2. The third inequality in the Lemma follows from the second one, since 2 W , DX BJ\I (Y, Z) 2 2 2 = DX,Y gJ\I (Z, W ) + DX,Z gJ\I (Y, W ) − DX,W gJ\I (Y, Z) . 6. Lemma. 9 there exist constants c8 , c9 , ˆ such that on any domain UI ⊂ Hn the and c10 depending just on n, h, d0 , and N following estimates hold for any i, i1 , i2 ∈ I with i1 = i2 1/2 (i) Pi GJ\I (1l − Pi ) (ii) Pi BJ\I (1l − Pi )g. , (1l − Pi ) . t. g0 . ´ ` 1 SEMINAIRES & CONGRES , . 41 ANALYTIC MANIFOLDS OF NONPOSITIVE CURVATURE Proof.

ABRESCH V. SCHROEDER converges to p∞ in Hn . 9 ), it is easy to compute the asymptotic behaviour of g ∧ g and T in the limit where pµ → p∞ . 16) (g ∧ g)(vj0 , ξj0 ; ξj0 , vj0 )|pµ ∼ η 2 xj0 (pµ )−1 and ∼ Tj0 (vj0 , ξj0 ; ξj0 , vj0 )|pµ T (vj0 , ξj0 ; ξj0 , vj0 )|pµ ∼ η 2 xj0 (pµ )−2 . 15) implies that R# (vj0 , ξj0 ; ξj0 , vj0 )|pµ is bounded by const η 2 xj0 (pµ )−1 as µ → ∞. Hence, the leading order term in the expansion of Tj0 must cancel versus a suitable counterterm in B ∧ G−1 B. In order to get reasonable estimates for R# on a term by term basis, we need to perform this cancelation explicitly.

In fact, the estimates for LI and BJ\I are proportional to 1/2 1/2 η 2 . However, because of the factors xi1 xi2 (1 +xi1 ) xi ) −1/2 the straightforward bounds for BI −1/2 ∧ G−1 −(1l+GI )−1 (1 +xi2 ) −1/2 BI and BJ\I 1/2 and xi (1 + ∧ G−1 BI are still singular near the divisor. 6 ) actually contain a hidden zero of the same order, and so they only make a contribution to BI ∧ G−1 −(1l+G )−1 I sorbed into −g0 ∧ BI resp. BJ\I ∧ G−1 BI which is small enough to be ab- g0 ; (2) the remaining terms are of such a special nature that their contribution can still be dominated by ε(g0 ∧ g0 + ΦI ) despite the fact that it is singular.

Download PDF sample

Rated 4.61 of 5 – based on 50 votes