Il professore Massimo Grossi dell’università di Roma la Sapienza il giorno giovedì 11 dicembre 2025 alle ore 15.00 nella sala riunioni del primo livello del dma terrà un seminario dal titolo:

Title: On the critical points of solutions of elliptic equations

Abstract: In this seminar we will study the shape of positive solutions to semilinear elliptic Dirichlet problems defined in a bounded domain of R^n. The first eigenfunction of the Laplacian and the solution to the torsion problem will serve as excellent toy models. A classical question we will address is the following: how does the geometry of the domain influence the number of critical points of the solutions?

We will also examine the case of Dirichlet problems on manifolds.

Seminario di Analisi – Martedi 13 Gennaio, ore 15, Aula G II livello DMA

Alberto Roncoroni – Politecnico di Milano

Rigidity results for critical elliptic equations

In this talk I will present some classification results for positive solutions to some classical critical elliptic equations in the Euclidean and Riemannian setting.

This is a joint work with G. Catino and D.D. Monticelli (Politecnico di Milano).

Moreover, if time permits, I will present some classification results in the sub-Riemannian setting.

These are joint works with G. Catino, D.D. Monticelli (Politecnico di Milano), Y.Y. Li (Rutgers University) and X. Wang (Michigan State University).

Seminario di Analisi – Martedi 13 Gennaio, ore 16, Aula G II livello DMA

Giovanni Catino – Politecnico di Milano

Manifolds with spectral Ricci lower bounds via conformal method and applications

In this talk, I will present recent generalizations of some classical theorems in Riemannian geometry to the setting of manifolds with spectral Ricci lower bounds. The results rely on a conformal method, inspired by classical papers of Schoen-Yau and Fischer-Colbrie. I will also present several applications of these techniques, in particular to the classification of stable minimal hypersurfaces. These are joint works with X. Cabrè (ICREA/Universitat de Barcelona), L. Mari, P. Mastrolia (Università degli Studi di Milano) and A. Roncoroni (Politecnico di Milano).