Mass of rays on complete open surfaces

Katsuhiro Shiohama, Takashi Shioya and Minoru Tanaka

Vol. 143 (1990), No. 2, 349–358

DOI: 10.2140/pjm.1990.143.349

Abstract

The total curvature of a complete open surface describes certain properties of the Riemannian structure which defines it. We study relationships between the total curvature and the mass of rays on a finitely connected complete open surface and obtain some integral formulas.

Mathematical Subject Classification 2000

Primary: 53C20

Secondary: 53C45

Milestones

Received: 4 February 1988

Published: 1 June 1990