On perturbations of the DN map of a disk causing changes of surface topology
Dmitrii Korikov
TL;DR
This paper investigates how perturbations in the Dirichlet-to-Neumann (DN) map of a disk can lead to changes in the surface's topology, specifically causing degeneration of the associated Riemann surface.
Contribution
It demonstrates the degeneration of the Schottky double of a genus 1 Riemann surface with boundary as its DN map approaches that of the unit disk, revealing topological effects of boundary data perturbations.
Findings
Degeneration of Schottky double as DN map approaches disk
Topological changes linked to boundary data perturbations
Connection between DN map perturbations and surface topology
Abstract
We establish the degeneration of the Schottky double of a genus 1 Riemann surface with boundary as its DN map tends to the DN map of the unit disk.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Quasicrystal Structures and Properties