Manifolds with group actions and elliptic operators
Author(s)
Bibliographic Information
Manifolds with group actions and elliptic operators
(Memoirs of the American Mathematical Society, v. 540)
American Mathematical Society, 1994
Available at 20 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
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INTERNATIONAL CHRISTIAN UNIVERSITY LIBRARY図
NO.540410.8/A445m/no.54004771090,
410.8/A445m/no.54004771090
Note
"November 1994, volume 112, number 540 (end of volume)"--T.p
Includes bibliographical references (p. 76-78)
Description and Table of Contents
Description
This work studies equivariant linear second order elliptic operators P on a connected noncompact manifold X with a given action of a group G. The action is assumed to be cocompact, meaning that GV=X for some compact subset V of X. The aim is to study the structure of the convex cone of all positive solutions of Pu=0. It turns out that the set of all normalized positive solutions which are also eigenfunctions of the given G -action can be realized as a real analytic submanifold *G[0 of an appropriate topological vector space *H. When G is finitely generated, *H has finite dimension, and in nontrivial cases *G[0 is the boundary of a strictly convex body in *H. When G is nilpotent, any positive solution u can be represented as an integral with respect to some uniquely defined positive Borel measure over *G[0. Lin and Pinchover also discuss related results for parabolic equations on X and for elliptic operators on noncompact manifolds with boundary.
Table of Contents
Introduction Some notions connected with group actions Some notions and results connected with elliptic operators Elliptic operators and group actions Positive multiplicative solutions Nilpotent groups: extreme points and multiplicative solutions Nonnegative solutions of parabolic equations Invariant operators on a manifold with boundary Examples and open problems Appendix: analyticity of $\Lambda (\xi, \scr L)$ References.
by "Nielsen BookData"