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Item Details
| Title:
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MANIFOLDS WITH GROUP ACTIONS AND ELLIPTIC OPERATORS
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| By: |
Vladimir Ya Lin, Yehuda Pinchover |
| Format: |
Paperback |
| List price:
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£38.95 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821826042 |
| ISBN 13: |
9780821826041 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 January, 1994 |
| Series: |
Memoirs of the American Mathematical Society No. 540 |
| Pages: |
78 |
| Description: |
Studies equivariant linear second order elliptic operators $P$ on a connected noncompact manifold $X$ with a given action of a group $G$. This book presents the study the structure of the convex cone of various positive solutions of $Pu=0$. |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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