5 papers
Nondegenerate neck pinches along the mean curvature flow
Gábor Székelyhidi
We show that for generic smooth compact initial surfaces the mean curvature flow in has spherical or nondegenerate neck pinch singularities at the first singular tim…
Generic neck pinch singularities along 2D Lagrangian mean curvature flow
Gábor Székelyhidi
We introduce a notion of nondegenerate neck pinch singularity along the Lagrangian mean curvature flow of surfaces in a Calabi-Yau surface. We show that such singularities can occu…
Uniqueness in the Plateau problem near Quadratic cones
Vishnu Nandakumaran, Gábor Székelyhidi
We consider minimal hypersurfaces inside the unit ball whose boundary on the sphere is a small perturbation of the link of a minimizing quadratic cone. We show that such minimal su…
Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations
Gábor Székelyhidi
We study Calabi-Yau metrics on a projective manifold in Kähler classes converging to a semiample class given by a fibration. We show that the Gromov-Hausdorff limit of the metrics…
Singularity formations in Lagrangian mean curvature flow
Yang Li, Gábor Székelyhidi
We study singularities along the Lagrangian mean curvature flow with tangent flows given by multiplicity one special Lagrangian cones that are smooth away from the origin. Some res…