Heat kernel bounds on manifolds with cusps
The authors obtain pointwise upper bounds for the heat kernel of a Riemannian manifold with cusps. They discuss a class of manifolds which have bounded geometry with respect to a hyperbolic structure with cusps; these manifolds include asymptotically hyperbolic manifolds. They obtain upper bounds on the heat kernels which they believe to be nearly optimal. They use methods of Gross to derive the required bounds from suitable Sobolev inequalities and logarithmic Sobolev inequalities.
scientific article; zbMATH DE number 4024228
scientific article