TY - JOUR
T1 - Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifold
AU - Chang, Shu Cheng
AU - Kuo, Ting Jung
AU - Lai, Sin Hua
PY - 2011
Y1 - 2011
N2 - In this paper, we derive two subgradient estimates of the CR heat equation in a closed pseudohermitian 3-manifold which are served as the CR version of the Li-Yau gradient estimate. With its applications, we first get a subgradient estimate of the logarithm of the positive solution of the CR heat equation. Secondly, we have the Harnack inequality and upper bound estimate for the heat kernel. Finally, we obtain Perelman-type entropy formulae for the CR heat equation.
AB - In this paper, we derive two subgradient estimates of the CR heat equation in a closed pseudohermitian 3-manifold which are served as the CR version of the Li-Yau gradient estimate. With its applications, we first get a subgradient estimate of the logarithm of the positive solution of the CR heat equation. Secondly, we have the Harnack inequality and upper bound estimate for the heat kernel. Finally, we obtain Perelman-type entropy formulae for the CR heat equation.
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U2 - 10.4310/jdg/1324477409
DO - 10.4310/jdg/1324477409
M3 - Article
AN - SCOPUS:84862968723
SN - 0022-040X
VL - 89
SP - 185
EP - 216
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
IS - 2
ER -