Heat kernel estimates with application to compactness of manifolds

By Fuzhou Gong, Feng-Yu Wang. 2001

75 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1607f434469e2527b9610a73cd6efce9c0cef3c1

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆ (2007, methodology): “up to have worse long time behaviors. (2) Harnack inequalities of type (1.5) has many applications. For instance, for diﬀusions on manifolds it has been applied to study the heat kernel estimate (cf. [10]), log-Sobolev 3 inequalities and contractivities of the semigroup (cf. [18, 1, 15]), and entrop”
Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below (2006, methodology): “This inequality has been applied and further developed to the study of functional inequalities (see [1,22,27,29]), heat kernel estimates (see [4,10]), higher order eigenvalues (see [11,28,30]), transportation cost inequalities (see [5]), and short time behavior of transition probabilities (see [2,3,”
Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, unknown): “AMS Subject Classification: 60H15; 60J35; 47D07.”
Log-Harnack Inequality for Stochastic Differential Equations in Hilbert Spaces and its Consequences (2009, methodology): “ inequalities for the associated Dirichlet form, the hyper-/super-/ultracontractivity properties of the semigroup, strong Feller property as well as estimates on the heat kernel of the semigroup (cf. [8, 13, 15, 6] and references therein). To establish this inequality for diﬀusions with curvature un”
Heat Kernel Bounds on Metric Measure Spaces and Some Applications (2014, background): “≤ C(ǫ) tµ(B(y, √ t)) exp ( C2(ǫ)t − d(x,y)2 (4 +ǫ)t ) . This, together with Theorem 1.2 again, yields |∇pt(x,·)|(y) ≤ C(ǫ) √ tµ(B(y, √ t)) exp ( C2(ǫ)t − d(x,y)2 (4 +ǫ)t ) , as desired. Gong and Wang [20] established a characterization of compactness of Riemannian manifolds by using heat kernel boun”