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GEOMETRY OF POINCARE DOMAINS.

Alexander Stanoyevitch

出版	University of MICHIGAN, 1990
URL	http://books.google.com.hk/books?id=mv-QGwAACAAJ&hl=&source=gbs_api

註釋

In this thesis, we address the problem of characterizing Poincare domains geometrically. Our most complete results are in the case of simply connected planar domains. We also obtain some estimates for the "best constant" K (i.e., the smallest constant K) for which the Poincare inequality is valid for a given Poincare domain. We compute the best constants for the intervals on the line, and obtain explicit relationships between the best constant of a cartesian product of a pair of domains and those of the