Virginia Agostiniani
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.
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