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Hamid Hezari

  1. Inverse problems in spectral geometry.

    Wed, 08/31/2011 - 15:01 — SomNambul
    Authors: Kiril Datchev, Hamid Hezari
    Subjects: Spectral Theory
    Abstract

    In this survey we review positive inverse spectral and inverse resonant
    results for the following kinds of problems: Laplacians on bounded domains,
    Laplace-Beltrami operators on compact manifolds, Schr\"odinger operators,
    Laplacians on exterior domains, and Laplacians on manifolds which are
    hyperbolic near infinity.

  2. Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch.

    Mon, 07/04/2011 - 15:01 — SomNambul
    Authors: Hamid Hezari
    Subjects: Analysis of PDEs
    Abstract

    We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume
    of the nodal sets of eigenfunctions. Our result improves the recent results of
    Sogge-Zelditch and in dimension 3 gives a new proof for a recent result of
    Colding-Minicozzi.

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