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Explore Allard-type regularity theory for varifolds with prescribed contact angles in this 35-minute mathematical lecture delivered at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into advanced geometric measure theory as part of the comprehensive thematic programme on Free Boundary Problems, examining the regularity properties of varifolds that satisfy specific contact angle conditions along boundaries. Learn about the extension of classical Allard regularity results to this specialized setting, understanding how prescribed contact angle constraints influence the smoothness and structure of varifolds. Gain insights into the mathematical techniques used to establish regularity in this geometric variational context, building upon fundamental concepts in geometric analysis and free boundary theory.
