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On the $p$ -pseudoharmonic map heat flow

Department of Mathematics, Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei 10617, R.O.C., Taiwan

E-mail Address: scchang@math.ntu.edu.tw

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Yuxin Dong

School of Mathematics, Fudan University, Shanghai 200433, P. R. China

E-mail Address: yxdong@fudan.edu.cn

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, and

Yingbo Han

https://orcid.org/0000-0002-8206-4790

School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan, P. R. China

E-mail Address: hyb@xynu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0129167X20501049Cited by:0 (Source: Crossref)

Abstract

In this paper, we consider the heat flow for $p$ -pseudoharmonic maps from a closed Sasakian manifold $(M^{2 n + 1}, J, 𝜃)$ into a compact Riemannian manifold $(N^{m}, g_{i j})$ . We prove global existence and asymptotic convergence of the solution for the $p$ -pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold $N$ is non-positive. Moreover, without the curvature assumption on the target manifold, we obtain global existence and asymptotic convergence of the $p$ -pseudoharmonic map heat flow as well when its initial $p$ -energy is sufficiently small.

Keywords:

AMSC: 32V05, 32V20, 53C56

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