Translator Disclaimer
VOL. 34 | 2002 Solution to the Shadow Problem in 3-Space
Mohammad Ghomi

Editor(s) Kenji Fukaya, Seiki Nishikawa, Joel Spruck

Abstract

If a convex surface, such as an egg shell, is illuminated from any given direction, then the corresponding shadow cast on the surface forms a connected subset. The shadow problem, first studied by H. Wente in 1978, asks whether a converse of this phenomenon is true as well. In this report it is shown that the answer is yes provided that each shadow is simply connected; otherwise, the answer is no. Further, the motivations behind this problem, and some ramifications of its solution for studying constant mean curvature surfaces in 3-space (soap bubbles) are discussed.

Information

Published: 1 January 2002
First available in Project Euclid: 31 December 2018

zbMATH: 1031.53010
MathSciNet: MR1925735

Digital Object Identifier: 10.2969/aspm/03410129

Subjects:
Primary: 53A05
Secondary: 52A15, 53A02, 53C45

Rights: Copyright © 2002 Mathematical Society of Japan

PROCEEDINGS ARTICLE
14 PAGES


SHARE
Back to Top