Reference : Dimension-free Harnack inequalities for conjugate heat equations and their applicatio...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows
Cheng, Li-Juan [Hangzhou Normal University, Hangzhou, China > School of Mathematics]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
In press
Analysis and PDE
Mathematical Sciences Publishers
30 pp
Yes (verified by ORBilu)
[en] Let M be a differentiable manifold endowed with a family of complete Riemannian metrics g(t) evolving under a geometric flow over the time interval [0,T[. In this article, we give a probabilistic representation for the derivative of the corresponding conjugate semigroup on M which is generated by a Schrödinger type operator. With the help of this derivative formula, we derive fundamental Harnack type inequalities in the setting of evolving Riemannian manifolds. In particular, we establish a dimension-free Harnack inequality and show how it can be used to achieve heat kernel upper bounds in the setting of moving metrics. Moreover, by means of the supercontractivity of the conjugate semigroup, we obtain a family of canonical log-Sobolev inequalities. We discuss and apply these results both in the case of the so-called modified Ricci flow and in the case of general geometric flows.
Researchers ; Professionals

File(s) associated to this reference

Fulltext file(s):

Open access
Conjugate-heat-equation.pdfAuthor preprint219.65 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.