ΕΚΔΗΛΩΣΕΙΣ

ΣΕΜΙΝΑΡΙΟ ΕΦΑΡΜΟΣΜΕΝΗΣ ΑΝΑΛΥΣΗΣ & ΜΕΡΙΚΩΝ ΔΙΑΦΟΡΙΚΩΝ ΕΞΙΣΩΣΕΩΝ: ON THE SHAPE OF HYPERSURFACES WITH ALMOST CONSTANT MEAN CURVATURE

Friday 09 Απριλίου 2021
Σεμινάριο Εφαρμοσμένης Ανάλυσης & Μερικών Διαφορικών Εξισώσεων:  On the shape of hypersurfaces with almost constant mean curvature

Σεμινάριο Εφαρμοσμένης Ανάλυσης & Μερικών Διαφορικών Εξισώσεων

Σύνδεσμος:meet.google.com/sru-gxoc-gzw

Ημερομηνία: Παρασκευή 9/4/2021

Ώρα: 15:15

Ομιλητής: Giulio Ciraolo (Università degli studi di Milano)

Τίτλος: On the shape of hypersurfaces with almost constant mean curvature

Περίληψη: Alexandrov's theorem asserts that spheres are the only closed embedded hypersurfaces with constant mean curvature in the Euclidean space. In this talk we will discuss some quantitative versions of  Alexandrov's theorem.
In particular, we will consider a hypersurface with mean curvature close to a constant and quantitatively describe its proximity to a sphere or to a collection of tangent spheres of equal radii in terms of the oscillation of the mean curvature.
We will also discuss these issues for the nonlocal mean curvature, by showing a remarkable rigidity property of the nonlocal problem which prevents bubbling phenomena and proving the proximity to a single sphere.

Βιβλιογραφία:
1. G. Ciraolo, L. Vezzoni. A sharp quantitative version of Alexandrov's theorem via the method of moving planes. J. Eur. Math. Soc. (JEMS), 20 (2018), 261-299
2. G. Ciraolo, F. Maggi. On the shape of compact hypersurfaces with almost constant mean curvature. Comm. Pure Appl. Math., 70 (2017), 665-716 
3. G. Ciraolo, A. Figalli, F. Maggi, M. Novaga. Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. J. Reine Angew. Math. (Crelle's Journal), Volume 2018, Issue 741, 275–294.
4. G. Ciraolo, L. Vezzoni. Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space. Indiana Univ. Math. J., 69 (2020), 1105-1153.
5. G. Ciraolo, A. Roncoroni, L. Vezzoni. Quantitative stability for hypersurfaces with almost constant curvature in space forms. To appear in Ann. Mat. Pura Appl.