Remark on the Limit Case of Positive Mass Theorem for Manifolds with Inner Boundary

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature

In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and Witten, we prove the following theorem: For any compact manifold with boundary and nonnegative scalar curvature, if it is spin and its boundary can be isometrically embedded into Euclidean space as a stric...

Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface

We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be C across a hypersurface Σ. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem [8] still holds on these manifolds if a geometric boundary condition is satisfied by metrics separated by Σ.

On two classes of third order boundary value problems with finite spectrum

‎The spectral analysis of two classes of third order boundary value problems is investigated‎. ‎For every positive integer $m$ we construct two classes of regular third order boundary value problems with at most $2m+1$‎ ‎eigenvalues‎, ‎counting multiplicity‎. ‎These kinds of finite spectrum results are previously known only for even order boundary value problems‎.