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On the L^p Spectrum of the Laplacian on Riemannian Manifolds

Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube

Tags

Spectral Theory Courses Functional Analysis Courses Differential Forms Courses Riemannian Manifolds Courses

Course Description

Overview

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Explore a comprehensive lecture on the $L^p$ spectrum of the Laplacian on differential forms. Delve into the resolvent set of the Laplacian on $L^p$ integrable $k$-forms, discovering how it lies outside a parabola for manifolds with exponential volume growth rate, without the need for bounded geometry. Examine sufficient conditions for a Weyl criterion to hold on the $L^p$-spectrum of the Laplacian on $k$-forms in open Riemannian manifolds. Gain insights into the detailed description of the $L^p$ spectrum of the Laplacian on $k$-forms over hyperbolic space. Learn about recent findings on the $L^p$ spectrum of conformally compact manifolds. This 59-minute talk by Nelia Charalambous from the University of Cyprus, presented at the Institut des Hautes Etudes Scientifiques (IHES), offers a deep dive into advanced mathematical concepts and recent research results in spectral theory.

Syllabus

Nelia Charalambous - On the $L^p$ spectrum


Taught by

Institut des Hautes Etudes Scientifiques (IHES)

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