Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I

By Steve Zelditch. 2011

49 citations recorded by the source corpus.

We develop analogues for Grauert tubes of real analytic Riemannian manifolds (M,g) of some basic notions of pluri-potential theory, such as the Siciak extremal function. The basic idea is to use analytic continuations of eigenfunctions in place of polynomials or sections of powers of positive line bundles for pluripotential theory. The analytically continued Poisson-wave kernel plays the role of Bergman kernel. The main results are Weyl laws in the complex domain, distribution of complex zeros of eigenfunctions on locally symmetric spaces, and estimates of triple products of eigenfunctions.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a75cd403f9a537aeba19a600126337fd1e28d692

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

  1. Steve Zelditch
  2. Zhiqin Lu
  3. Bernard Shiffman
  4. Kento Fujita
  5. G. Kokarev
  6. Boris Hanin
  7. Y. Canzani
  8. Chin-Yu Hsiao

In Geometry and Topology

  1. Steve Zelditch
  2. Zhiqin Lu
  3. Bernard Shiffman
  4. Kento Fujita
  5. Chin-Yu Hsiao
  6. Robert J. Berman
  7. G. Marinescu
  8. Xiaonan Ma

Citations in the corpus