An operator algebra associated with a pair of intersecting manifolds

变维相交流形上图 Dirichlet 能量与图 Laplacian 的收敛性

Convergence of graph Dirichlet energies and graph Laplacians on intersecting manifolds of varying dimensions

针对不同内在维数相交流形并集，论文证明归一化图 Dirichlet 能量可同时适应各维数并发生 Γ-收敛与谱收敛，而未归一化能量仅反映最高维流形。

The Semiclassical Resolvent on Conic Manifolds and Application to Schrödinger Equations

In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent kernel is the sum of b-pseudodifferential operators, scattering pseudodifferential operators and intersecting Legendrian distributions. As an application, we shall establish Strichartz estimates for Schrödinger equations on non-compact manifolds with multiple non-product conic singularities.

Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds

In this article we study the linearized anisotropic Calderón problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderón problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial…

The linearized Calderon problem in transversally anisotropic geometries

In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an FBI type transform at certain points in the transversal manifold. This leads to recovery of transversal singularities in the linearized problem. The method requires a geometric condition on the transversal manifold related to pairs of intersecting geodesics, but it does not involve the geodesic…