A Green’s function proof of the positive mass theorem and related topics

Abstract: In this talk, we will explore the role of harmonic and p-harmonic functions in establishing fundamental geometric inequalities in mathematical relativity, such as the positive mass theorem and the Penrose inequality. We will introduce new monotonicity formulas along the level flow of these functions, which provide simple proofs for these inequalities. Additionally, we will discuss how these formulas can be used to characterize the nonnegativity of the scalar curvature, suggesting a synthetic notion of this concept applicable in non-smooth contexts.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )

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JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

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