Year: 2025
Type: preprint
Abstract: In this paper, we introduce the regularized conformal heat flow of $n$-harmonic maps, or simply regularized $n$-conformal heat flow from $n$-dimensional Riemannian manifold. This is a system of evolution equations combined with regularized $n$-harmonic map flow and a metric evolution equation in conformal direction. For $n=2$, the conformal heat flow does not develop finite time singularity unlike usual harmonic map flow \cite{P23} (Park, 2024). In this paper, we show the analogous result, that regularized $n$-conformal heat flow does not develop finite time singularity unlike the (regularized) $n$-harmonic map flow.
Source: arXiv (Cornell University)
Author: Park, Woongbae
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407683995