On an old conjecture of Almgren

Abstract: In this talk I will give an overview on the few results available on the conjecture of Almgren regarding the convexity of drops subject to the action of an external potential. In particular I will present recent progress in this direction obtained with G. De Philippis on their connectedness. Together with an older result of McCann, this answers positively the conjecture in dimension two. The proof is inspired by the two-point function technique introduced by B. Andrews and is reminiscent of the doubling of variables trick in the context of viscosity solutions.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

Lisbon webinar in analysis and differential equations

Series comments: The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field. All seminars will take place in the Zoom platform. The links for the planned seminars can be found at: wade.ulisboa.pt/ In order to get the password to access the seminars, please subscribe the announcements in the registration menu wade.ulisboa.pt/registration, or contact one of the organizers.

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