# Online seminar "The isoperimetric inequality outside convex sets"

## TopMath Online Seminar with Prof. Nicola Fusco (Analysis)

Prof. Nicola Fusco (Università degli Studi di Napoli) is a worldwide well-known mathematician, author of many influential papers on Calculus of Variations, Geometric Measure Theory and the theory of Partial Differential Equations. He is also author, together with L. Ambrosio and D. Pallara, of one of the best seller books in mathematics: “Functions of Bounded Variation and Free Discontinuity Problems” (Oxford Science Publications 2000). He is recipient of the 1994 Caccioppoli Prize, the 2013 Amerio Prize and has been invited speaker both at the European Congress of Mathematics and at the International Congress of Mathematicians. He has been recently awarded the Humboldt Research Award.

In collaboration with TopMath, Prof. Fusco offers an online seminar on "The isoperimetric inequality outside convex sets" every Thursday, 4 PM - 5:30 PM, from November 11th to December 23rd. The event aims at all interested master's and doctoral students in mathematics.

For the abstract of the online seminar see here.

### Program:

**Lecture 1 (11.11.): **Basic definitions and properties of sets of finite perimeter, coarea formula, De Giorgi's structure theorem, the euclidean isoperimetric inequality.

**Lecture 2 (18.11.):** The relative isoperimetric inequality in a half space. First variation of volume and perimeter. The capillarity functional. Young's law.

**Lecture 3 (25.11.): **Spherically convex sets, Kuratowski convergence, Normal cones and restricted normal cones. Normal bundle and restricted normal bundle.

**Lecture 4 (02.12.): **The total curvature. An estimate of the total curvature of a set. A Willmore type inequality.

**Lecture 5 (09.12.):** Lambda-minimizers of the perimeter. Density estimates. Regularity of Lambda-minimizers.

**Lecture 6 (16.12.):** Proof of the relative isoperimetric inequality outside a convex set.

**Lecture 7 (23.12.):** Characterization of the equality cases in the relative inequality outside a convex set.

**Lecture 8 (13.01.)**

### Registration

Please **register by November 10th**, 2021 (write to: topmath@ma.tum.de), You will receive the Zoom login data in the week of November 8th, 2021.