Geometry and Topology Seminar —— On the Lawson-Osserman conjecture on the minimal surfaces system
报告人：Jonas Hirsch(University of Leipzig)
时间：2025-01-10 09:30-10:30
地点：智华楼225(四元厅)
【摘要】
In the renowned paper by Lawson and Osserman, non-existence, non-uniqueness, and irregularity of solutions to the minimal surface system, Conjecture 2.1 stands out: Conjecture 2.1: The systems (2.2) and (2.3) are equivalent for any locally Lipschitz function f on Ω. Here (2.2) is the full minimal surface system
while (2.3) involves only the outer variations:
We affirmatively resolve the conjecture in dimension two. Our main result can be succinctly stated as follows:
Theorem: Let f: B1 ⊂ R2 → Rn be a Lipschitz critical point of the area func tional concerning outer variations, then f is smooth.
Having presented the conjecture and our result, the remainder of the talk will be devoted to outlining the ideas behind the proof and elucidating the role of working in two dimensions. It is a joint work with Connor Mooney and Riccardo Tione.
