GRADIENT ESTIMATE OF HEAT EQUATION FOR HARMONIC MAP ON NONCOMPACT MANIFOLDS y
Hyun Jung Kim
Abstract
Hyun Jung Kim
Abstract
aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K ) is a complete Riemannian manifold with sectional curvature bounded above by a constant > 0. Let u : is a heat equation for harmonic map. We estimate the energy density of u.
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aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K ) is a complete Riemannian manifold with sectional curvature bounded above by a constant > 0. Let u : is a heat equation for harmonic map. We estimate the energy density of u.
Key concepts: Mathematics, Ricci curvature, Sectional curvature, Harmonic map, Bounded function, Riemannian manifold, Manifold (fluid mechanics), Heat equation