Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds

More precisely, we show that the minimax optimal orders of magnitude L d/(d+2) T (d+1)/(d+2) of the regret bound over T time instances against an environment whose mean-payoff

On the analyticity of the semigroups generated by the Hodge-Laplacian, and by the Stokes and Maxwell operators on Lipschitz subdomains of

Taylor, Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem, J. Pazy, Semigroups of Linear Operators and Applications

It already possesses some features that are typical of more general sub-Riemannian structures: the Hausdorff dimension is bigger than the topological dimension, the cut locus and

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest two-dimensional Riemannian

One shows that the Riesz transform is L p bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain L

In case 3, (D) is again obvious since such a manifold has polynomial volume growth, (DUE) is well-known (it can be extracted from the work of Varopoulos, see for instance [99],

Motivated by applications to machine learning and imaging science, we study a class of online and stochastic optimization problems with loss functions that are not Lipschitz