Deadline: 16 nov 2023

The aim of this research is to enhance our comprehension of geometric partial differential equations and their connection to the underlying curvature assumptions. Firstly, we intend to explore the relationship between the level-set flow of p-harmonic functions, the torsion problem with Dirichlet boundary data, and the Mean Curvature Flow. Secondly, we aim to study monotonicity formulas, with the dual objective of refining our understanding of existing formulas, deriving new geometric and functional inequalities on one hand, and on the other, exploring the existence of genuinely new monotonicity formulas.

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