CAPACITY FUNCTIONS IN RIEMANNIAN SPACES.
CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS
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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 Greens 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
- Theoretical Mathematics