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PreprintarXiv licencearXiv

Parabolic defect measures for Harmonic Maps with Free Boundary

  • Anirban Das
  • Ali Hyder
  • Yannick Sire
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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.

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Cite

BibTeXRIS
BibTeX
@misc{das2026parabolic,
  title = {{Parabolic defect measures for Harmonic Maps with Free Boundary}},
  author = {Anirban Das and Ali Hyder and Yannick Sire},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14050},
  eprint = {2609.14050},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14050},
}
RIS
TY  - UNPB
TI  - Parabolic defect measures for Harmonic Maps with Free Boundary
AU  - Anirban Das
AU  - Ali Hyder
AU  - Yannick Sire
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.14050
UR  - https://arxiv.org/abs/2609.14050
AB  - 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.
ER  -