Isoperimetric inequalities and curvature of level sets for harmonic functions on smooth and singular surfaces

Abstract: One of the main themes of the talk are monotonicity formulas for level sets of harmonic functions in Euclidean domains and Riemannian surfaces, including the singular Alexandrov surfaces. Such formulas allow for studying the logarithmic convexity of the length of the level curves and related isoperimetric type inequalities. Related are the studies of the geodesic curvature of the level curves and of the steepest descent.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php