For every given β<0, we study the problem of maximizing the first Robin eigenvalue of the Laplacian λβ(Ω) among convex (not necessarily smooth) sets Ω⊂Sn with fixed perimeter. In particular, denoting by σn the perimeter of the n-dimensional hemisphere, we show that for fixed perimeters P<σn, geodesic balls maximize the eigenvalue. Moreover, we prove a quantitative stability result for this isoperimetric inequality in terms of volume difference between Ω and the ball D of the same perimeter.
A Spectral Isoperimetric Inequality on the n-Sphere for the Robin-Laplacian with Negative Boundary Parameter
Acampora P.;
2025-01-01
Abstract
For every given β<0, we study the problem of maximizing the first Robin eigenvalue of the Laplacian λβ(Ω) among convex (not necessarily smooth) sets Ω⊂Sn with fixed perimeter. In particular, denoting by σn the perimeter of the n-dimensional hemisphere, we show that for fixed perimeters P<σn, geodesic balls maximize the eigenvalue. Moreover, we prove a quantitative stability result for this isoperimetric inequality in terms of volume difference between Ω and the ball D of the same perimeter.File in questo prodotto:
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