分野別セミナー

In this talk we extend fine properties of convex functions in the Euclidean spaces to sub-Riemannian manifolds. We first review the notion and basic properties of horizontal convex functions in the Heisenberg group. We next give a natural definition of horizontal convex envelopes of continuous functions and provide several concrete examples. The notion of convex envelope can be applied to understand horizontal convexity of viscosity solutions to various nonlinear PDEs in the Heisenberg group. It time permits, we will also discuss regularity of the horizontal convex envelope.

リンク：セミナーHP
　　　　福岡大学セミナーハウスへのアクセス