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AN ENERGY DENSITY ESTIMATE OF HEAT EQUATION FOR HARMONIC MAP

Hyun Jung Kim
한국수학교육학회|2011.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제1호|pp. 79-86

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참고문헌

키워드

energy densityheat equation for harmonic mapLiouville Theorem.
주제분류수학

초록

Suppose that (M, g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by ¡K · 0 and (N, g) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : M x [0,∞) ! N be the solution of a heat equation for harmonic map with a bounded image. We estimate the energy density of u.

Abstract

Suppose that (M, g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by ¡K · 0 and (N, g) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : M x [0,∞) ! N be the solution of a heat equation for harmonic map with a bounded image. We estimate the energy density of u.

참고문헌 (12)

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  7. R.S. Hamilton, "A Matrix Harnack Estimate for the Heat Equation", Comm. Anal. Geom, 1, pp.113~126 (1993)
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  9. P. Li, "On he Parabolic Kernel of the Schroedinger operator", Acta Math, 156, pp.153~201 (1986)
  10. P. Li, "The Heat Equation and Harmonic Maps of Complete Manifolds", Invent. Math, 105, pp.1~46 (1991)
  11. G.G. Liao, "On the Heat Equation for Harmonic Maps from Non-compact Manifolds"
  12. R. Scheon, "Lectures on Differential Geometry", pp.1~23 (1995), International Press

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