談話会


2019/6/24(Mon)

16:30--17:30 理学部 E404/406/408 大セミナー室

稲濱 譲

九州大学 数理学研究院

Heat trace asymptotics for equiregular sub-Riemannian manifolds

We study a ``div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our proof is probabilistic. In particular, we use S. Watanabe's distributional Malliavin calculus. Our main result holds true for any smooth measure on the manifold, but it has a spectral geometric meaning when Popp's measure is considered. Although our result may not be extremely new from a probabilistic viewpoint, we believe that it is an important progress in sub-Riemannian geometry. (This is a joint work with Setsuo Taniguchi (Kyushu University))