Conformal mappings and first eigenvalue of Laplacian on surfaces

TL;DR

This paper establishes a straightforward relationship between conformal mappings and the first eigenvalue of the Laplacian on surfaces embedded in Euclidean space, providing insights into spectral geometry.

Contribution

It introduces a simple relation connecting conformal maps and Laplacian eigenvalues on surfaces, advancing understanding in spectral geometry.

Findings

Derived a relation linking conformal maps to Laplacian eigenvalues

Simplified the analysis of spectral properties of surfaces

Potential applications in geometric analysis and physics

Abstract

In this note we give a simple relation between conformal mapping and the first eigenvalue of Laplacian for surfaces in Euclidean spaces.