Analysis Aspects of Minimal Surfaces Spring 2020

The talks are now recorded. The videos are available here.
Some notes written by the speakers are available in the schedule table below (providing notes is not compulsory).


Prof. Dr. Tristan Rivière, Alessandro Pigati


The goal of the seminar is to present the (by now) classical regularity theory for area minimizing codimension one minimal surfaces.
In the course of the seminar we will go through fundamental notions from geometric measure theory (rectifiability, coarea formula, finite perimeter sets, currents, varifolds, ...), as well as classical notions from elliptic regularity theory (excess decay, Caccioppoli/reverse Poincaré inequality, harmonic approximations, tangent cones, Federer's dimension reduction argument, ...).
One of the goals will be to have a completely explained proof of the smoothness of perimeter minimizing sets up to ambient dimension 7, and to explain why dimension 8 is a bifurcation point in the regularity theory.


A good knowledge of Sobolev functions in several variables (as provided, e.g., by Functional Analysis I/II) is recommended. Basic notions from differential geometry will be also assumed.


Due to the limited number of places, in order to participate to this reading seminar you have to register on myStudies. The deadline for the registration is February 13.

Where and when

The talks will take place every Thursday, from 13.15 to 15.00, in the Hermann Weyl Zimmer (HG G 43).

Schedule of the talks

The following is a provisional schedule of the talks. The first few ones will be given by the organizers, then the participants will speak (a couple every week).

Week numberDateTopicSpeakerNotes
1February 20Rectifiable setsTristan Rivière.pdf
2February 27Sets of finite perimeterYujie Wu.pdf
3March 12De Giorgi's structure theoremRiccardo Caniato.pdf
4March 19First variation of area and monotonicity. Regularity of almost flat stationary sets: tilt-excess inequalityAlessandro Pigati.pdf [last updated April 23]
5March 26Regularity of almost flat stationary sets: Lipschitz and harmonic approximationAlessandro Pigati(same file)
6April 2Regularity of almost flat stationary sets: conclusion. Proof of monotonicity formulaAlessandro Pigati(same file)
7April 9Currents and varifolds: first variation, monotonicity and its consequences. Compactness of rectifiable and integral varifolds
Anthony Salib
8April 23Regularity of "multiplicity one" varifolds with small excess
David Morselli.pdf
9April 30Generalized varifolds and a rectifiability criterion by Ambrosio-SonerMatteo Giardi
10May 7Minimality of the Simons coneMatilde Gianocca
11May 14Improved regularity for area-minimizing currents in codimension one (a.k.a. perimeter-minimizing sets), part ISeyed Ali Naseri Sadr
12May 28Improved regularity for area-minimizing currents in codimension one, part IIAlireza Ataei

If you see your name misspelled, or assigned to the wrong week, please send an email to Alessandro Pigati.