Generalized convex sets and shadows problem

2015/01/27 by Yu. B. Zelinskii, Yurii Zelinskii, I. Yu. Vyhovs’ka +5 · 2 citations
Business, Management and Accounting · Mathematics · #FOS: Mathematics #Facility Location and Emergency Management #Metric Geometry (math.MG) #math.MG

paper · pdf · doi:10.48550/arxiv.1501.06747

arxiv created 2015/01/27 · openalex publication_date 2015/01/27 · arxiv updated 2015/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of shadow is solved. It is equivalent to condition for point is in generalized convex hull of a family of compact sets.

Cited by

• On the shadow problem for domains in the Euclidean spaces
• On the shadow problem and its generalizations to ellipsoids

Related

• On weakly m-convex sets
• Generalizations of the shadow problem
• Shadows and convexity of surfaces
• Regularity of shadows and the geometry of the singular set associated to a Monge-Ampere equation
• Shadows of convex bodies