Title: Uniqueness of tangent planes at infinite time for collapsed self-translating solitons

Abstract: The main goal of this talk is to prove the uniqueness of the asymptotic planes of complete translating solitons with finite genus, width, and entropy. If time allows, we will also provide some applications of this uniqueness result. This is joint work with Francisco Martin and Niels M. Møller.

Title: Rotational Weingarten hypersurfaces in R^{n+1}: classification and sharp inequalities

Abstract: In this talk, first we provide a classification result for a class of complete rotational Weingarten hypersurfaces in the Euclidean space. Second, we prove sharp inequalities for the norm of the second fundamental form of a class of Weingarten hypersurfaces. We show that sharpness is attained by a cylinder of the Euclidean space.

Title: Lower estimates for the squared norm of the second fundamental form via the first eigenvalue of the p-Laplacian

Abstract: This talk presents a suitable Bochner formula for a certain divergence-type operator. As an application, we establish an integral inequality involving the squared norm of the second fundamental form of a minimal submanifold (with or without boundary) in the sphere and the first eigenvalue of the p-Laplacian.

Title: Star-shaped CMC surfaces bounded by a circle

Abstract: In 1853, J. H. Jellet proved that the only closed star-shaped CMC surfaces in the Euclidean three space is a round sphere [Jel]. As a boundary version's of Jellet's Theorem, López conjectured that planar disks and spherical caps are the only star-shaped CMC surfaces in \mathbb{R}^3 bounded by a circle [Lop]. In this talk, we present a proof that this conjecture is true under an assumption regarding the position of the surface's star-center in relation to its circular boundary.

References

[Jel] Jellet, J. H., Sur la surface dont la courbature moyenne est constant. J. Math. Pures Appl., 18 (1853), 163--167.
[Lop] López, R., Constant mean curvature surfaces with boundary. Springer-Verlag Berlin Heidelberg, 2013.

Title: Geometric obstructions for phase transitions and comparison of min-max theories for minimal hypersurfaces

Abstract: The Allen-Cahn equation is a semilinear partial differential equation that serves as a mathematical model for the evolution of phase separation and pattern formation phenomena, and whose stationary solutions approximate minimal hypersurfaces.

In this talk, we will present new examples concerning the (non)existence of certain equilibrium solutions of this PDE in connection to degenerate minimal hypersurfaces, and discuss how these examples relate to a classical theorem by Frankel about minimal surfaces in nonnegatively curved spaces. We will also comment on some consequences regarding the comparison between Almgren-Pitts and Allen-Cahn approaches to min-max theories for such hypersurfaces.

This is joint work with Jingwen Chen (University of Pennsilvania).

Title: TBA

Abstract: TBA

Title:  Observações sobre variedades m-quasi-Einstein

Abstract: Consideremos uma variedade Riemanniana M fechada m-quasi-Einstein, com campo vetorial associado X. Mostraremos que a curvatura escalar de M é constante se, e somente se, X é Killing. Abordaremos ainda a condição na qual X é livre de divergência.