Free Boundary Minimal Surfaces in Geodesic Balls in Hyperbolic Space and Upper Half-Sphere

Explore the intricacies of free boundary minimal surfaces in geodesic balls within hyperbolic space and the upper half-sphere in this 58-minute seminar from the Spectral Geometry in the clouds series. Delve into Vladimir Medvedev's extension of Lima and Menezes' work, connecting free boundary minimal immersions in spherical cap geodesic balls to maximal metrics for a functional on Riemannian metrics. Examine the application to hyperbolic space geodesic balls and critical metrics for a higher-order generalization of the Lima-Menezes functional. Investigate implications for the area index of free boundary minimal surfaces in both hyperbolic space and upper half-sphere geodesic balls, based on Medvedev's recent research. Gain insights into cutting-edge mathematical concepts at the intersection of differential geometry and analysis.