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GRADIENT ESTIMATE OF HEAT EQUATION FOR HARMONIC MAP ON NONCOMPACT MANIFOLDS  

Kim, Hyun-Jung (Department of Math., Hoseo University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.5_6, 2010 , pp. 1461-1466 More about this Journal
Abstract
aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K < 0 and (N, $\bar{b}$) is a complete Riemannian manifold with sectional curvature bounded above by a constant $\mu$ > 0. Let u : $M{\times}[0,\;{\infty}]{\rightarrow}B_{\tau}(p)$ is a heat equation for harmonic map. We estimate the energy density of u.
Keywords
heat equation for harmonic map; sectional curvature;
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