完备流形上带位势的热核估计

Abstract

Abstract:

First the author gets a gradient estimate of the heat eq uation's positive solution with potential on a complete manifold which is not compact; secondly, the author uses the technique of geodesic to get Harnack inequ alities;moreover, the author eatablishes two integral inequalities; together wi th Harnack inequalities, the author gets the upper and lower bounds of heat ker nels; at last, the author uses function's result to dominant heat kernel of p forms.
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Key words: Potential, Heat equation, Fundamental solution, Harnack , inequality

CLC Number:

53C40

WANG Lin-Feng. Estimates of Heat Kernel with Potential on Complete Manifold[J].Acta mathematica scientia,Series A, 2004, 4(6): 699-713.

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References

[1]Davies E B. Heat Kernels and Spectral Theory.Cambridge: Cambridge University Press,1989

[2]Li P, Yau ST. On the parabolic kernel of the Schrodinger operat or. Acta Math, 1986,156: 153-201

[3]Scheon R, Yau ST. Lectures on Differential Geometry. Combridge: International Press, 1994

[4]David Gilbarg, Neil S, Trudinger. Elliplic Partial Differential Equations of Second Order.Berlin Heidelberg: Springer Verlag, 2001

[5]Issac Chavel. Eigenvalus in Riemannian Geometry.Orleads: Academic Press,1984

[6]Cheng SY, Li P, Yau ST. Heat equations on Minimal Submanifolds and Their Applications. Manuscript

[7]Bueler E. The heat kernel with weighted hodge Laplacian on noncompact manifolds. Trons Amer Math Soc, 1999, 351: 683-713

[8]Jose F. Escobar&Alexandre Freire, the spectrum of the lplacian of manifol ds of positive curvature. Duke Math J, 1992, 65(1): 1-21

[9]Jose F. Escobar&Alexandre Freire, the differential form spectrum of mani folds of positive curvature. Duke Math J,1993, 69(1): 1-41

[10]Harold Donnelly, Peter Li. Lower bounds for the eigenvalues of rie mannian manifolds. Michigan Math J,1982, 29: 149-161

[11]Harold Donnelly, Peter Li. Lower bounds for the eigenvalues of negative ly curved manifolds. Math Z, 1980, 172: 29-40

[12]Isaac Chavel. Riemannian Geometry:A Modern Introdution.Cambridge: Cambridge University Press,1993

[13]Cheeger J, Ebin D G. Comparison Theorens in Riemannian Geometry.Netherlands: NorthHolland Publishing Company, 1975

[14]Eschanburg J H. Comparison theorems and hypersurfaces.Manuscripta Math, 1987, 59: 295-323

[15]Reed M, Simon B. Method of Modern Mathematical Physical. New York: Func tional Analysis Academic Press, 1972

[16]伍鸿熙. 微分几何中的Bochner技巧（上）. 数学进展，1981, 10(1) : 57-76

[17]伍鸿熙. 微分几何中的Bochner技巧（下）. 数学进展，1982, 11(1) : 19-61

[18]白正国，沈一兵. 黎曼几何初步. 北京: 高等教育出版社，1992

Estimates of Heat Kernel with Potential on Complete Manifold

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