Related papers: Spectral gap on Riemannian path space over static …

In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci curvature on the base manifold; this work was motivated by a…

We prove the existence of spectral gaps of Ornstein-Uhlenbeck operators on loop spaces over a class of Riemannian manifolds which include hyperbolic spaces. This is an alternative proof and an extension of a result in Chen-Li-Wu in J.…

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…

For sub-Riemannian manifolds with a chosen complement, we first establish the derivative formula and integration by parts formula on path space with respect to a natural gradient operator. By using these formulae, we then show that upper…

On a fairly general class of Riemannian manifolds M, we prove lower estimates in terms of the Ricci curvature for the spectral bound (when M has infinite volume) and for the spectral gap (when M has finite volume) for the Laplace-Beltrami…

We introduce the $R$ cut-off covering spectrum and the cut-off covering spectrum of a complete length space or Riemannian manifold. The spectra measure the sizes of localized holes in the space and are defined using covering spaces called…

We prove quantitative unique continuation estimates for relatively dense sets and spectral subspaces associated to small energies of Schr\"odinger operators on Riemannian manifolds with Ricci curvature bounded below. The upper bound for the…

In this paper, we extend the sharp lower bounds of spectal gap, due to Chen- Wang [10, 11], Bakry-Qian [6] and Andrews-Clutterbuck [5], from smooth Riemaniannian manifolds to general metric measure spaces with Riemannian curvature-dimension…

Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is presented. The shifts are allowed to be in the Cameron-Martin…

We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space $X$. This is done by finite dimensional approximation. In particular we prove…

We provide a simplified proof of the existence, under some assumptions, of a spectral gap for the Perron-Frobenius operator of piecewise uniformly expanding maps on Riemannian manifolds when acting on some Sobolev spaces. Its consequences…

For a second order operator on a compact manifold satisfying the strong H\"ormander condition, we give a bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian of a Riemannian manifold. We consider a wide class…

We prove sharp spectral gap estimates on compact manifolds with integral curvature bounds. We generalize the results of Kr\"oger (Kr\"oger '92) as well as of Bakry and Qian (Bakry-Qian '00) to the case of integral curvature and confirm the…

Let $M$ be a connected, noncompact, complete Riemannian manifold, consider the operator $L=\DD +\nn V$ for some $V\in C^2(M)$ with $\exp[V]$ integrable w.r.t. the Riemannian volume element. This paper studies the existence of the spectral…

We investigate the compact submanifolds in Riemannian space forms of nonnegative sectional curvature that satisfy a lower bound on the Ricci curvature, that bound depending solely on the length of the mean curvature vector of the immersion.…

When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but lower bounded by a continuous function, we give a new characterization of this lower bound through the convexity of relative entropy on the…

In this paper, we will present some characterizations for the upper bound of the Bakry-Emery curvature on a Riemannian manifold by using functional inequalities on path space. Moreover, some characterizations for general lower and upper…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

We consider a rigidity problem for the spectral gap of the Laplacian on an $RCD(K,\infty)$-space (a metric measure space satisfying the Riemannian curvature-dimension condition) for positive $K$. For a weighted Riemannian manifold,…

In this short note, we find a new gap phenomena on Riemannian manifolds, which says that for any complete noncompact Riemannian manifold with nonnegative Ricci curvature, if the scalar curvature decays faster than quadratically, then it is…