Work

Unique Continuation for Locally Uniformly Distributed Measures

Year: 2025

Type: article

Abstract: In this note we show that the support of a locally k-uniform measure in $${\mathbb {R}}^{n+1}$$ R n + 1 satisfies a kind of unique continuation property. As a consequence, we show that locally uniformly distributed measures satisfy a weaker unique continuation property. This continues work of Kirchheim and Preiss (Math Scand 90(1): 152-160, 2002) and David, Kenig and Toro (Comm Pure Appl Math 54(4): 385-449, 2001) and lends additional evidence to the conjecture proposed by Kowalski and Preiss (J Reine Angew Math 379: 115-151, 1987) that each connected component of the support of a locally n-uniform measure in $${\mathbb {R}}^{n+1}$$ R n + 1 is contained in the zero set of a quadratic polynomial.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-025-01978-6

Authors: Max Engelstein, Ignasi Guillén-Mola

Institutions: University of Minnesota, Universitat Autònoma de Barcelona

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290