Manifolds with group actions and elliptic operators / Vladimir Ya. Lin, Yehuda Pinchover.

Format:

Book

Author/Creator:

Lin, Vladimir I͡Akovlevich, 1935- author.

Pinchover, Yehuda, 1953- author.

Series:

Memoirs of the American Mathematical Society ; Volume 112, Number 540.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 112, Number 540

Language:

English

Subjects (All):

Elliptic operators.

Group actions (Mathematics).

Manifolds (Mathematics).

Physical Description:

1 online resource (90 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1994.

Language Note:

English

Summary:

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.

Contents:

""Table of Contents""; ""1. Introduction""; ""2. Some notions connected with group actions""; ""3. Some notions and results connected with elliptic operators""; ""4. Elliptic operators and group actions""; ""5. Positive multiplicative solutions""; ""6. Nilpotent groups: extreme points and multiplicative solutions""; ""7. Nonnegative solutions of parabolic equations""; ""8. Invariant operators on a manifold with boundary""; ""9. Examples and open problems""; ""10. Appendix: analyticity of A(Î?L)""; ""References""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0119-3