Special Year 2018-19: Variational Methods in Geometry - Seminar

We review various recent results aimed at understanding bubbling into spheres for boundaries with almost constant mean curvature. These are based on joint works with Giulio Ciraolo (U Palermo), Matias Delgadino (Imperial College London), Brian...

We will describe recent progress on the existence theory and asymptotic analysis for solutions of the complex Ginzburg-Landau equations on closed manifolds, emphasizing connections to the existence of weak minimal submanifolds of codimension two. On...

For an immersed minimal surface in $R^3$, we show that there exists a lower bound on its Morse index that depends on the genus and number of ends, counting multiplicity. This improves, in several ways, an estimate we previously obtained bounding the...

It is fundamental to understand a manifold with positive scalar curvature and its topology. The minimal surface approach pioneered by R. Schoen and S.T. Yau have advanced our understanding of positively curved manifolds. A very important result is...

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...