Shadows and convexity of surfaces

2004/09/20 by Mohammad Ghomi
Mathematics · #math.DG #msc:53A05 #msc:53A04 #msc:52A15 #msc:53C42

paper · pdf

published as Ann. of Math. (2), Vol. 155 (2002), no. 1, 281--293 · 13 pages, published version

arxiv created 2004/09/20 · arxiv updated 2009/12/01

Abstract

We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the ``shadow problem" formulated by H. Wente.

Related

• On weakly m-convex sets
• Generalized convex sets and shadows problem
• Generalizations of the shadow problem
• Regularity of shadows and the geometry of the singular set associated to a Monge-Ampere equation
• Function-theoretic properties for the Gauss maps of various classes of surfaces