23 citations · 73 across the 11 of their papers we have counts for
14 papers
Index and nullity of minimal surfaces via representation theory
Mikhail Karpukhin, Mario B. Schulz
We develop a representation-theoretic approach to determine the Morse index and nullity of an embedded minimal surface based only on its topology and symmetry group. The method com…
A new family of minimal surfaces of even genus in the three-dimensional sphere
Mario B. Schulz, David Wiygul
We discover a family of closed, embedded minimal surfaces in the three-dimensional round sphere which includes new examples with low genus. The existence proof relies on an equivar…
Index growth not imputable to topology
Alessandro Carlotto, Mario B. Schulz, David Wiygul
We employ partitioning methods, in the spirit of Montiel--Ros but here recast for general actions of compact Lie groups, to prove effective lower bounds on the Morse index of certa…
Disc stackings and their Morse index
Alessandro Carlotto, Mario B. Schulz, David Wiygul
We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the…
Topological control for min-max free boundary minimal surfaces
Giada Franz, Mario B. Schulz
We establish general bounds on the topology of free boundary minimal surfaces obtained via min-max methods in compact, three-dimensional ambient manifolds with mean convex boundary…
Spectral estimates for free boundary minimal surfaces via Montiel-Ros partitioning methods
Alessandro Carlotto, Mario B. Schulz, David Wiygul
We adapt and extend the Montiel-Ros methodology to compact manifolds with boundary, allowing for mixed (including oblique) boundary conditions and also accounting for the action of…
Infinitely many pairs of free boundary minimal surfaces with the same topology and symmetry group
Alessandro Carlotto, Mario B. Schulz, David Wiygul
The topology and symmetry group of a free boundary minimal surface in the three-dimensional Euclidean unit ball do not determine the surface uniquely. We provide pairs of non-isome…
Noncompact self-shrinkers for mean curvature flow with arbitrary genus
Reto Buzano, Huy The Nguyen, Mario B. Schulz
In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. Here, we employ min-max techniques to give a rigor…
Minimal hypertori in the four-dimensional sphere
Alessandro Carlotto, Mario B. Schulz
We prove that the four-dimensional round sphere contains a minimally embedded hypertorus, as well as infinitely many, pairwise non-isometric, immersed ones. Our analysis also yield…
Free boundary minimal surfaces with connected boundary and arbitrary genus
Alessandro Carlotto, Giada Franz, Mario B. Schulz
We employ min-max techniques to show that the unit ball in contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
Incomplete Yamabe flows and removable singularities
Mario B. Schulz
We study the Yamabe flow on a Riemannian manifold of dimension minus a closed submanifold of dimension and prove that there exists an instantaneously complete solution…
Unconditional existence of conformally hyperbolic Yamabe flows
Mario B. Schulz
We prove global existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension starting from any smooth, conformally hyperbolic initial metr…
Yamabe flow on non-compact manifolds with unbounded initial curvature
Mario B. Schulz
We prove global existence of Yamabe flows on non-compact manifolds of dimension under the assumption that the initial metric is conformally equivalent to…
Instantaneously complete Yamabe flow on hyperbolic space
Mario B. Schulz
We prove global existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension . The initial metric is assumed to be conformally hyperbolic w…