相关论文: Bilaplacian on a Riemannian manifold and Levi-Civi…

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower…

We extend the notion of a Thomas projective connection (a projective equivalence class of linear connections) for supermanifolds. As a by-product, we arrive at a generalisation of the multidimensional Schwarzian derivative for the super…

In this paper, we continue to study some applications with respect to a Reilly type integral formula associated with the $\phi$-Laplacian. Some inequalities of Brascamp-Lieb type and Colesanti type are provided.

We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or…

We show the linear drift of the Brownian motion on the universal cover of a closed connected Riemannian manifold is $C^{k-2}$ differentiable along any $C^{k}$ curve in the manifold of $C^k$ metrics with negative sectional curvature. We also…

A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation…

For a subRiemannian manifold and a given Riemannian extension of the metric, we define a canonical global connection. This connection coincides with both the Levi-Civita connection on Riemannian manifolds and the Tanaka-Webster connection…

Extensions of the fractional Brownian fields are constructed over a complete Riemannian manifold. This construction is carried out for the full range of the Hurst parameter $\alpha\in(0,1)$. In particular, we establish existence,…

We give a geometric description of the motion of eigenvalues of a Brownian motion with values in some matrix spaces. In the second part we consider a paper by Polya where he introduced a function close to the Riemann zeta function, which…

We reconstruct a Riemannian manifold and a Hermitian vector bundle with compatible connection from the hyperbolic Dirichlet-to-Neumann operator associated with the wave equation of the connection Laplacian. The boundary data is local and…

We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a Riemann surface with boundaries. A small-mass expansion gives back the Liouville action in the massless limit, while the…

Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.

Let $\{g_t\}_{t\in [0,T)}$ be a family of complete time-depending Riemannian matrics on a manifold which evolves under backwards Ricci flow. The It\^{o} formula is established for the $\mathcal{L}$-distance of the $g_t$-Brownian motion to a…

We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of…

Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge the classical framework of the convolution algebra for…

The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$ is a stochastic process that models a random perturbation of the geodesic flow. If $M$ is a orientable compact constantly curved surface, we show that in the…

In this note, we combine the two approaches of Billingsley (1998) and Cs\H{o}rg\H{o} and R\'ev\'esz (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a Brownian motion whose time space is…

We generalize the Benjamini-Pemantle-Peres estimate relating hitting probability and Martin capacity to the setting of manifolds with Ricci curvature bounded below. As applications we obtain: (1) a sharp estimate for the probability that…

For $d \geq 2$ let $B$ be standard $d$-dimensional Brownian motion. For any $\alpha < 1/d$ we construct an $\alpha$-H\"{o}lder continuous function $f \colon [0,1] \to \mathbb{R}^d$ so that the range of $B-f$ covers an open set. This…

In this paper, we prove new rigidity results related to some generalised Ricci-Hessian equation on Riemannian manifolds.