Year: 2026
Type: article
Abstract: The geometric tangent cone to a probability measure μ is a set of measure-valued applications that are almost geodesics. This is a nonlocal condition, typically lost when conditioning the measure on a given set. We show that if one removes the barycenter of any element of the tangent cone, then the resulting set of centered measure fields is characterized by a local condition. Precisely, centered tangent fields must be concentrated on a family of vector subspaces attached to any point, and these subspaces correspond to the normal spaces to some sets of “dimension k ” on which the measure μ is concentrated.
DOI: 10.5802/jep.355
Author: Averil Aussedat
Institution: University of Pisa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Agence Nationale de la Recherche
OpenAlex ID: W7221995631