Work

Parabolic defect measures for Harmonic Maps with Free Boundary

Year: 2026

Type: preprint

Abstract: We introduce defect measures for the heat flow of a class of harmonic maps with free boundary and initiate their analysis. Our flow is motivated by singular perturbations on the boundary of the domain, emphasizing structural differences between harmonic maps with free boundary and their classical counterpart. The harmonic maps we consider are a reformulation of maps introduced by Da Lio and Rivière and arise in several problems in the spectral geometry of Steklov eigenvalues. Contrary to the classical case, the flow we consider exhibits features of global nature and the blow-up analysis turns out to be much more challenging.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.14050

Authors: Das, Anirban, Hyder, Ali, Sire, Yannick

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Department of Atomic Energy, Government of India

Awards: Regularity Versus Singularity Formation in Nonlinear Partial Differential Equations, G240064222

OpenAlex ID: W7213370111

Cites: 2

Cited by:

Related to: 10