Heat Flows with Prescribed Singularities from 3-dimensional Manifold

Jie Ji; Jingru Niu

Heat Flows with Prescribed Singularities from 3-dimensional Manifold

Analysis of PDEs 2024-12-20 v1

Authors: Jie Ji , Jingru Niu

Abstract

In this paper, we study singular heat flows from a 3-dimensional complete bounded Riemannian manifold without boundary into the hyperbolic space with prescribe singularity along a closed curve. We prove the existence and regularity of the singular heat flows. Furthermore, we prove that the singular heat flows converge to a singular harmonic map at an exponential rate.

Keywords

geometric flows hyperbolic 3-manifolds geodesic flow

Cite

@article{arxiv.2412.14634,
  title  = {Heat Flows with Prescribed Singularities from 3-dimensional Manifold},
  author = {Jie Ji and Jingru Niu},
  journal= {arXiv preprint arXiv:2412.14634},
  year   = {2024}
}