Alain Haraux*
Abstract. This paper is devoted to a strange looking question: is it possible to deduce the shape of a smooth convex set by measuring at each point the distance of the horizon standing at a fixed height h? The question is surprisingly difficult and we only have partial results.
Keywords: convex sets, curvature, distance.
MSC: 52A10, 52A15, 53B99.
DOI 10.56082/annalsarscimath.2025.1.47
*Sorbonne Universite, Universite Paris Diderot SPC, CNRS, INRIA, Laboratoire Jacques-Louis Lions, LJLL, F-75005, Paris, France, alain.haraux@sorbonne-universite.fr
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 1, 2025
