We prove that the systole (or more generally, any k-th homology
systole) of a minimal surface in an ambient three manifold of
positive Ricci curvature tends to zero as the genus of the minimal
surfaces becomes unbounded. This is joint work with Anna...
We shall present a procedure which to any admissible family of
immersions of surfaces into an arbitrary closed riemannian
manifolds assigns a smooth, possibly branched, minimal surface
whose area is equal to the width of the corresponding minmax
and...
Mean curvature flow is the negative gradient flow of the volume
functional which decreases the volume of (hyper)surfaces in the
steepest way. Starting from any closed surface, the flow exists
uniquely for a short period of time, but always develops...
In this talk I would like to explain how methods from symplectic
geometry can be used to obtain sharp systolic inequalities. I will
focus on two applications. The first is the proof of a conjecture
due to Babenko-Balacheff on the local systolic...
Minimal surfaces are critical points of the area functional. In
this talk I will discuss classification results for minimal
surfaces with index one in 3-manifolds with non-negative Ricci
curvature and outline the proof that in spherical space
forms...
The lecture will discuss recent joint work with C. Bellettini
and O. Chodosh. The work taken together establishes sharp
regularity conclusions, compactness and curvature estimates for any
family of codimension 1 integral $n$-varifolds satisfying:
(i...
Renormalized volume (and more generally W-volume) is a geometric
quantity found by volume regularization. In this talk I'll describe
its properties for hyperbolic 3-manifolds, as well as discuss
techniques to prove optimality results.
In the 90's, Gromov and Schoen introduced the theory of harmonic
maps into singular spaces, in particular Euclidean buildings, in
order to understand p-adic superrigidity. The study was quickly
generalized in a number of directions by a number of...
I will first survey some recent progress on global problems
related to scalar curvature and area/volume, focusing in particular
on scale breaking phenomena in such problems. I will then discuss
the role of the Hawking mass in the resolution of this...
