Small eigenvalues of surfaces
We show that the Laplacian of a Riemannian metric on a closed surface S with Euler characteristic χ(S) < 0 has at most -χ(S) small eigenvalues.
math.DG↗
arXiv subjects
Werner Ballmann
Publications and source records attributed to Werner Ballmann.
Index theorems on manifolds with straight ends
We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume.
math.DG↗
Boundary Value Problems for Elliptic Differential Operators of First Order
We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.
math.DG↗
Regularity and index theory for Dirac-Schrödinger systems with Lipschitz coefficients
Dirac-Schrödinger systems play a central role when modeling Dirac bundles and Dirac-Schrödinger operators near the boundary, along ends or near other singularities of Riemannian manifolds. In this article we develop the Fredholm theory of Dirac-Schrödinger systems with Lipschitz coefficients.
math.AP↗
Eigenvalues and Holonomy
We estimate the eigenvalues of connection Laplacians in terms of the non-triviality of the holonomy.
math.DG↗