Related papers: Heat content asymptotics for sub-Riemannian manifo…

By establishing the intrinsic super-Poincar\'e inequality, some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive. These conditions, as well as the…

This paper studies the heat content} for Schr\"odinger operators of the fractional Laplacian $(-\Delta)^{\alpha/2}$, $0<\alpha\leq 2$ in $R^d$, $d\geq 1$. Employing probabilistic and analytic techniques, a small time asymptotic expansion…

We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domain $$\Omega = (-1,1)\times\mathbb{T}\times\mathbb{T}$$ taking as observation regions slices of the form $\omega=(a,b) \times…

We propose a novel approach for studying small-time asymptotics of the fractional heat content of $C^2$ non-characteristic domains in Carnot groups. Denoting the sub-Laplacian operator by $\mathcal{L}$, the fractional heat content of a…

We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and…

We introduce a new method for computing the heat invariants of a 2-dimensional Riemannian manifold based on a result by S.Agmon and Y.Kannai. Two explicit expressions for the heat invariants are presented. The first one depends on the…

We study a spatial asymptotic behaviour at infinity of kernels $p_t(x)$ for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient conditions under which the limits $$ \lim_{r \to \infty}…

We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a…

In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…

Rapidly rotating Rayleigh-B\'enard convection is studied by combining results from direct numerical simulations (DNS), laboratory experiments and asymptotic modeling. The asymptotic theory is shown to provide a good description of the bulk…

We study the law of a hypoelliptic Brownian motion on an infinite-dimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous…

$H$-type foliations $(\mathbb{M},\mathcal{H},g_{\mathcal{H}})$ are studied in the framework of sub-Riemannian geometry with bracket generating distribution defined as the bundle transversal to the fibers. Equipping $\mathbb{M}$ with the…

For a given bounded domain $\Omega\subset {\Bbb R}^n$ with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the heat trace associated with the Stokes operator as $t\to 0^+$. These…

We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note is the introduction of a concept of mildly degenerate…

We are concerned with stochastic processes on surfaces in three-dimensional contact sub-Riemannian manifolds. Employing the Riemannian approximations to the sub-Riemannian manifold which make use of the Reeb vector field, we obtain a second…

Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the local extrinsic and intrinsic curvature. We show that the…

We study and classify smooth bounded domains in an analytic Riemannian manifold which are critical for the heat content at all times t>0. We do that by first computing the first variation of the heat content, and then showing that a domain…

We study measures associated to Brownian motions on infinite-dimensional Heisenberg-like groups. In particular, we prove that the associated path space measure and heat kernel measure satisfy a strong definition of smoothness.

We address two linked problems at the interface of quantum topology and number theory: deriving asymptotic expansions of the Witten--Reshetikhin--Turaev invariants for 3-manifolds and establishing quantum modularity of false theta…

The purpose of this paper is to study gradient estimate of Hamilton - Souplet - Zhang type for the general heat equation $$ u_t=\Delta_V u + au\log u+bu $$ on noncompact Riemannian manifolds. As its application, we show a Harnak inequality…