arXiv research

The paper estimates the gap between eigenvalues of a clamped plate problem.

Study Witten deformation on noncompact manifolds with bounded geometry.

We calculate heat invariants of arbitrary Riemannian manifolds without boundary. Every heat invariant is expressed in terms of powers of the Laplacian and the distance function. Our approach is based on a multi-dimensional generalization of the Agmon-Kannai method. An application to computation of the Korteweg-de Vries…

Study shows exponential decay of Bergman kernels on manifolds with bounded Ricci curvature.

We introduce a new method for computing the heat invariants of a 2-dimensional Riemannian manifold based on a result by S.Agmon and Y.Kannai. Two explicit expressions for the heat invariants are presented. The first one depends on the choice of a certain coordinate system; the second involves only invariant terms but h…

We give a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations including the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon-Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman…

We give a proof of the Donnelly-Fefferman growth bound of Laplace-Beltrami eigenfunctions which is probably the easiest and the most elementary one. Our proof also gives new quantitative geometric estimates in terms of curvature bounds which improve and simplify previous work by Garofalo and Lin. The proof is based on …

Uniform Shapiro-Lopatinski conditions ensure well-posedness of boundary value problems on manifolds with bounded geometry.

Proves well-posedness of mixed Robin boundary value problem on manifolds with bounded geometry.

Analyzes tunneling effects for Schrödinger operators on vector bundles.

Paper compares higher torsions and removes fiberwise Morse function assumption.