Related papers: Strichartz estimates for the Dirac equation on asy…

Gromov proved a quadratic decay inequality of scalar curvature for a class of complete manifolds. In this paper, we prove that for any uniformly contractible manifold with finite asymptotic dimension, its scalar curvature decays to zero at…

We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in $n+1$ dimensions for odd $n$ and obtain improved estimates in even dimensions. This is achieved by deriving local smoothing estimates for certain…

Schultz \cite{S98} proved dispersive estimates for the wave equation on lattice graphs $\mathbb{Z}^d$ for $d=2,3,$ which was extended to $d=4$ in \cite{BCH23}. By Newton polyhedra and the algorithm introduced by Karpushkin \cite{K83}, we…

In this paper, we study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. We adopt the frequency domain method to prove that the system with smooth initial data is…

We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix…

Following the previous work [1], we investigate the impact of damping on the oscillation of smooth solutions to some kind of quasilinear wave equations with Robin and Dirichlet boundary condition. By using generalized Riccati transformation…

This paper aims to give a general (possibly compact or noncompact) analog of Strichartz inequalities with loss of derivatives, obtained by Burq, G\'erard, and Tzvetkov [19] and Staffilani and Tataru [51]. Moreover we present a new approach,…

We establish Strichartz estimates for the Schr\"odinger equation on Riemannian manifolds $(\Omega,\g)$ with boundary, for both the compact case and the case that $\Omega$ is the exterior of a smooth, non-trapping obstacle in Euclidean…

We review some recent results concerning lower eigenvalues estimates for the Dirac operator [6, 7]. We show that Friedrich's inequality can be improved via certain well-chosen symmetric tensors and provide an application to Sasakian spin…

We introduce a class of rotationally invariant manifolds, which we call \emph{admissible}, on which the wave flow satisfies smoothing and Strichartz estimates. We deduce the global existence of equivariant wave maps from admissible…

We derive estimates relating the values of a solution at any two points to the distance between the points, for quasilinear isotropic elliptic equations on compact Riemannian manifolds, depending only on dimension and a lower bound for the…

We obtain an $L^4$ space-time Strichartz inequality for any smooth three-dimensional Riemannian manifold $(M,g)$ which is asymptotically conic at infinity and non-trapping, where $u$ is a solution to the Schr\"odinger equation $iu_t + {1/2}…

We prove under a weak smoothness condition that two Riemannian manifold are isomorphic if and only there exists an order isomorphism which intertwines with the Dirichlet type heat semigroups on the manifolds.

In this paper, the existence and uniqueness of foliations by constant mean curvature spheres on asymptotically flat manifolds of nonzero ADM mass in all dimensions were established. (A similar result in the case of positive mass was…

We consider the gravity-capillary waves in any dimension and in fluid domains with general bottoms. Using the paradiferential reduction established in the companion paper, we prove Strichartz estimates for solutions to this problem, at a…

We study the Schr\"odinger equation on a flat euclidean cone $\mathbb{R}_+ \times \mathbb{S}^1_\rho$ of cross-sectional radius $\rho > 0$, developing asymptotics for the fundamental solution both in the regime near the cone point and at…

Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this paper we prove a direct analogue of that result in all…

We prove uniform $L^p$ resolvent estimates for the stationary damped wave operator. The uniform $L^p$ resolvent estimates for the Laplace operator on a compact smooth Riemannian manifold without boundary were first established by Dos Santos…

We establish Strichartz estimates (both reversed and some direct ones), pointwise decay estimates, and weighted decay estimates for the linear wave equation in dimension two with an almost scaling-critical potential, in the case when there…

We consider an asymptotically flat Lorentzian manifold of dimension (1,3). An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality…