Finite-Time Blow-up for the Heat Flow of Pseudoharmonic Maps

In this paper, we consider the heat flow for pseudoharmonic maps from a closed pseudohermitian manifold (M2n+1, J, θ) into a compact Riemannian manifold (Nm, g). In our pervious work, we proved global existence of the solution for the pseudoharmonic map heat flow, provided that the sectional curvatu...

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Bibliographic Details
Published in:Indiana University mathematics journal 2015-01, Vol.64 (2), p.441-470
Main Authors: Chang, Shu-Cheng, Chang, Ting-Hui
Format: Article
Language:English
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Summary:In this paper, we consider the heat flow for pseudoharmonic maps from a closed pseudohermitian manifold (M2n+1, J, θ) into a compact Riemannian manifold (Nm, g). In our pervious work, we proved global existence of the solution for the pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold N is nonpositive. In this present paper, we show that the solution of the pseudoharmonic map heat flow blows up in finite time if the initial map belongs to a nontrivial homotopy class and its initial energy is sufficiently small. As a consequence, we obtain global existence for the pseudoharmonic map heat flow without the curvature assumption on the target manifold.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2015.64.5499