Accession Number : AD0633082

Title :   CAPACITY FUNCTIONS IN RIEMANNIAN SPACES.

Descriptive Note : Technical rept.,

Corporate Author : CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s) : Ham Ow,Wellington

Report Date : JUN 1966

Pagination or Media Count : 71

Abstract : The existence of the capacity function in an arbitrary noncompact Riemannian space is proved and the capacity is then defined for boundary components as well as the ideal boundary. Moreover, the capacity function of the ideal boundary is shown to possess certain extremal properties. An equivalence relation between the capacity of the ideal boundary, the Green's function, and the harmonic measure of the ideal boundary is given. Certain criteria are given which then enable one to determine under what conditions the capacity of a boundary component is zero. The extremal length of a family of curves is discussed and certain basic theorems involving it are stated. (Author)

Descriptors :   (*ALGEBRAIC TOPOLOGY, *POTENTIAL THEORY), (*FUNCTIONS(MATHEMATICS), ALGEBRAIC TOPOLOGY), BOUNDARY VALUE PROBLEMS, GREEN'S FUNCTIONS, MEASURE THEORY

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE