On the analytic reflection of a minimal surface

Jaigyoung Choe

Vol. 157 (1993), No. 1, 29–36

DOI: 10.2140/pjm.1993.157.29

Abstract

For a long time it has been known that in a Euclidean space one can reflect a minimal surface across a part of its boundary if the boundary contains a line segment, or if the minimal surface meets a plane orthogonally along the boundary. The proof of this fact makes use of H. A. Schwarz’s reflection principle for harmonic functions.

In this paper we show that a minimal surface, as a conformal and harmonic map from a Riemann surface into R³, can also be reflected analytically if it meets a plane at a constant angle.

Mathematical Subject Classification 2000

Primary: 53A10

Secondary: 30F15

Milestones

Received: 20 December 1989

Published: 1 January 1993