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This note is motivated by gradient estimates of Li-Yau, Hami\-lton, and Souplet-Zhang for heat equations. In this paper, our aim is to investigate Yamabe equations and a non linear heat equation arising from gradient Ricci soliton. We will apply Bochner technique and maximal principle to derive gradient estimates of the general non-linear heat equation on Riemannian manifolds. As their consequence, we give several applications to study heat equation and Yamabe equation such as Harnack type inequalities, gradient estimates, Liouville type results.
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참고문헌 (14)
참고문헌 신청
M.-F. Bidaut-Veron / 1991 / Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations / Invent. Math 106(3):489~539
L. Brandolini / 1998 / Positive solutions of Yamabe type equations on complete manifolds and applications / J. Funct. Anal 160(1):176~222
Q. Chen / 2012 / Existence and Liouville theorems for V -harmonic maps from complete manifolds / Ann. Global Anal. Geom 42(4):565~584
Q. Chen / 2014 / Omori-Yau maximum principles, V -harmonic maps and their geometric applications / Ann. Global Anal. Geom 46(3):259~279
Q. Chen / 2015 / A maximum principle for generalizations of harmonic maps in Hermitian, affine, Weyl, and Finsler geometry / J. Geom. Anal 25(4):2407~2426
L. Brandolini / 1998 / Positive solutions of Yamabe type equations on complete manifolds and applications / J. Funct. Anal 160(1):176~222
Q. Chen / 2012 / Existence and Liouville theorems for V -harmonic maps from complete manifolds / Ann. Global Anal. Geom 42(4):565~584
Q. Chen / 2014 / Omori-Yau maximum principles, V -harmonic maps and their geometric applications / Ann. Global Anal. Geom 46(3):259~279
Q. Chen / 2015 / A maximum principle for generalizations of harmonic maps in Hermitian, affine, Weyl, and Finsler geometry / J. Geom. Anal 25(4):2407~2426
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