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The local structure of nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds

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Abstract

Let (M, g) be a 3-dimensional Riemannian manifold without boundary. Consider the solution of Schrödinger equation onM. We show that locally there exists an injective Lipschitz continuous map from the nodal set of the solution away from a finite union of some small solid cones, which only intersect at the common vertex, into itself and the image set stays on a finite union of some 2-dimensional cones which have a common vertex. Moreover, the singular set of the solution is contained in the union of the solid cones.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    Jingyi Chen

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  1. Jingyi Chen
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Chen, J. The local structure of nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds. Manuscripta Math 85, 255–263 (1994). https://doi.org/10.1007/BF02568197

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  • DOI: https://doi.org/10.1007/BF02568197

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