On the concentration-compactness phenomenon for the first Schrodinger eigenvalue

TL;DR

This paper investigates how extremal potentials for the first Schrödinger eigenvalue behave on closed Riemannian surfaces, focusing on their concentration-compactness properties.

Contribution

It provides new insights into the concentration-compactness phenomena for extremal potentials associated with the first Schrödinger eigenvalue on Riemannian surfaces.

Findings

Characterization of concentration-compactness behavior of extremal potentials

Identification of conditions leading to concentration phenomena

Analysis of variational sequences for the first Schrödinger eigenvalue

Abstract

We study a variational problem for the first Schrodinger eigenvalue on closed Riemannian surfaces. More precisely, we explore concentration-compactness properties of sequences formed by its extremal potentials.