相关论文: Stochastic processes on surfaces in three-dimensio…

We investigate hypersurfaces M isometrically immersed in an (n+1)-dimensional semi-Riemannian space of constant curvature, n > 3, such that the operator A^3, where A is the shape operator of M, is a linear combination of the operators A^2…

We construct a parametrix of a resolvent of elliptic differential operators acting on half-densities on manifolds with ends. The construction is carried out by introducing suitable pseudodifferential operators compatible with the end…

In this paper we examine the geometry of minimal surfaces of arithmetic hyperbolic 3-manifolds. In particular, we give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial…

Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…

This is the first paper of a series in which we plan to study spectral asymptotics for sub-Riemannian Laplacians and to extend results that are classical in the Riemannian case concerning Weyl measures, quantum limits, quantum ergodicity,…

Riemann-Hilbert problems are jump problems for holomorphic functions along given interfaces. They arise in various contexts, e.g. in the asymptotic study of certain nonlinear partial differential equations and in the asymptotic analysis of…

Fang-Wu\cite{FW17} presented a explicit spectral gap for the O-U process on path space over a Riemannian manifold without boundary under the bounded Ricci curvature conditions. In this paper, we will extend these results to the case of the…

We formulate the Riemannian calculus of the probability set embedded with $L^2$-Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold)…

This is the second in a series of papers on the numerical treatment of hyperelliptic theta-functions with spectral methods. A code for the numerical evaluation of solutions to the Ernst equation on hyperelliptic surfaces of genus 2 is…

We study sequences of immersions respecting bounds coming from Riemannian geometry and apply the ensuing results to the study of sequences of submanifolds of symplectic and contact manifolds. This allows us to study the subtle interaction…

We consider Carleson-Sj\"{o}lin operators on Riemannian manifolds that arise naturally from the study of Bochner-Riesz problems on manifolds. They are special cases of H\"{o}rmander-type oscillatory integral operators. We obtain improved…

Two-dimension almost-Riemannian structures of step 2 are natural generalizations of the Grushin plane. They are generalized Riemannian structures for which the vectors of a local orthonormal frame can become parallel. Under the 2-step…

We investigate some topological properties of random geometric complexes and random geometric graphs on Riemannian manifolds in the thermodynamic limit. In particular, for random geometric complexes we prove that the normalized counting…

We study a stochastic primal-dual method for constrained optimization over Riemannian manifolds with bounded sectional curvature. We prove non-asymptotic convergence to the optimal objective value. More precisely, for the class of…

High-dimensional data with intrinsic low-dimensional structure is ubiquitous in machine learning and data science. While various approaches allow one to learn a data manifold with a Riemannian structure from finite samples, performing…

In this paper we show that, for a sub-Laplacian $\Delta$ on a $3$-dimensional manifold $M$, no point interaction centered at a point $q_0\in M$ exists. When $M$ is complete w.r.t. the associated sub-Riemannian structure, this means that…

Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance…

We give curvature-dependant convergence rates for the optimization of weakly convex functions defined on a manifold of 1-bounded geometry via Riemannian gradient descent and via the dynamic trivialization algorithm. In order to do this, we…

We determine the Hamiltonian vector field on an odd dimensional manifold endowed with almost cosymplectic structure. This is a generalization of the corresponding Hamiltonian vector field on manifolds with almost transitive contact…

The purpose of this paper is to establish the well-posedness of the stochastic Stefan problem on moving hypersurfaces. Through a specially designed transformation, it turns out we need to solve stochastic partial differential equations on a…