東工大 数理解析セミナー： Ulrich Menne 氏
- Ulrich Menne 氏（国立台湾師範大学）
- A priori diameter bounds for solutions to a variety of Plateau problems
- Plateau's problem in Euclidean space may be given many distinct formulations with solutions to most of them admitting an associated varifold. This includes Reifenberg's approach based on sets and Čech homology as well as Federer and Fleming's approach using integral currents and their homology. Thus, we employ the unifying setting of varifolds to prove a priori bounds on the geodesic diameter in terms of boundary behaviour. A central challenge in this process is to determine a suitable notion of connectedness; in fact, there exist several possible definitions distinct already in the case of varifolds associated to smooth immersions. This is ongoing joint work with C. Scharrer.