Open Access Research

Harnack inequality for parabolic Lichnerowicz equations on complete noncompact Riemannian manifolds

Liang Zhao

Author Affiliations

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China

Boundary Value Problems 2013, 2013:190  doi:10.1186/1687-2770-2013-190

Published: 27 August 2013

Abstract

In this paper, we study the gradient estimates for positive solutions to the following parabolic Lichnerowicz equations

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on complete noncompact Riemannian manifolds, where h, p, q, A, B are real constants and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/190/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/190/mathml/M2">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/190/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/190/mathml/M3">View MathML</a>.

MSC: 58J05, 58J35.

Keywords:
Lichnerowicz equation; positive solutions; Harnack inequality