The Heat Flows of Harmonic Maps from $S^2$ to $S^2$

Asai, Keisui

Publication date

January 1996

Publisher

Graduate School of Mathematical Sciences, The University of Tokyo

Abstract

In this paper we show that the heat flow $u(x,t)$ with a rotationally symmetric initial map $u_0(x,t)$ converges to a harmonic map as $t\to\infty$ if $n=1$ and $0<π$ $(θ\in(0,π))$. Here we call $u_0:S^2 \to S^2$ rotationally symmetric if there exists a function $h:[0,π] \to R$ such that $h(0)=0,$ $h(π)=nπ,$ and $u(\cosτ\sinθ,\sinτ\sinθ,\cosθ) =(\cosτ\sin h(θ),\sinτ\sin h(θ),\cos h(θ)).

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The Heat Flows of Harmonic Maps from $S^2$ to $S^2$

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The Heat Flows of Harmonic Maps from $S^2$ to $S^2$

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