Semiclassical Asymptotics on Manifolds with Boundary

Details Semiclassical Asymptotics on Manifolds with Boundary Semiclassical Asymptotics on Manifolds with Boundary

2008-03-17

arxiv.org/abs/0803.2502v1

Mathematics

Spectral Theory

28 pages

Scientific paper

We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.

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