Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 43 min ago
PreprintCC BY 4.0arXiv

Partial regularity of heat flow of fractional harmonic maps to spheres

  • Hengrong Du
  • Tao Huang
  • Armin Schikorra
  • Changyou Wang
Open at sourcePDFDOICite

Abstract

In this paper, we introduce the notation of stationary heat flow of s-harmonic maps from Rm into the unit sphere π•Šβ„“βˆ’1β†ͺ ℝℓ, for 0<s<1, framed through the parabolic version of Caffarelli-Silvestre's extension. We prove that any stationary heat flow of s-harmonic maps is smooth away from a closed set of vanishing (m+2βˆ’2s)-dimensional parabolic Hausdorff measure. This extends to the fractional settings the partial regularity theorem on the heat flow of harmonic maps into spheres by Chen-Li-Lin and Feldman.

Related

  1. Partial Regularity of Stable Stationary Harmonic Maps into Compact Lie Groups
    Jacob Krantz
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. Boundary regularity of harmonic map heat flows from RCD spaces into CAT(0) spaces
    Zi-Ying Liu, Hui-Chun Zhang, Xi-Ping Zhu
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  3. Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation
    Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Harmonic maps from spheres with lowest possible index and their properties
    Surkov Egor
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Sharp Harmonic-Mean Bounds for Neumann Eigenvalues on Riemannian Surfaces and Counterexamples to Geodesic Ball Optimality on Higher-Dimensional Spheres
    Hongtao Hu, Meiqi Liu, Qiaoran Wu +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{du2026partial,
  title = {{Partial regularity of heat flow of fractional harmonic maps to spheres}},
  author = {Hengrong Du and Tao Huang and Armin Schikorra and Changyou Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29191},
  eprint = {2610.29191},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29191},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Partial regularity of heat flow of fractional harmonic maps to spheres
AU  - Hengrong Du
AU  - Tao Huang
AU  - Armin Schikorra
AU  - Changyou Wang
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29191
UR  - https://arxiv.org/abs/2610.29191
AB  - In this paper, we introduce the notation of stationary heat flow of s-harmonic maps from R^m into the unit sphere π•Š^β„“βˆ’1β†ͺ ℝ^β„“, for 0<s<1, framed through the parabolic version of Caffarelli-Silvestre's extension. We prove that any stationary heat flow of s-harmonic maps is smooth away from a closed set of vanishing (m+2βˆ’2s)-dimensional parabolic Hausdorff measure. This extends to the fractional settings the partial regularity theorem on the heat flow of harmonic maps into spheres by Chen-Li-Lin and Feldman.
ER  -