Accession Number:

AD0618987

Title:

CLASSIFICATION OF LOCALLY EUCLIDEAN SPACES,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV LOS ANGELES

Personal Author(s):

Report Date:

1964-03-08

Pagination or Media Count:

26.0

Abstract:

The classification of Riemann surfaces has largely reached its completion. The purpose of the present paper is to lay the foundation for a new intriguing field in the classification theory Riemannian spaces with Euclidean metrics. The paper is self-contained, both for the Riemann surface expert and the reader whose main interest is with higher dimensions. The significance of locally Euclidean spaces lies, first of all, in that their function-theoretic nature differs for dimensions n2 and n2. The existence or nonexistence of Greens functions and positive or bounded harmonic functions in Rn, punctured Rn, and in the punctured flat torus offer simple examples. A striking phenomenon is that, despite such differences, the basic inclusion relations remain valid. Moreover, capacities and null-classes can be defined for components of point sets in Rn.

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE