14 citations · 56 across the 15 of their papers we have counts for
15 papers
Morse index of Karcher saddle towers in
David Wiygul
For each integer Hermann Karcher identified a complete singly periodic minimal surface (unique up to similarity) with ends asymptotic to the union of plan…
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…
New low-genus desingularizations of three Clifford tori and related characterizations
Nikolaos Kapouleas, David Wiygul
For each nonnegative integer we construct in the round three-sphere a closed embedded minimal surface of genus which can be interpreted as a desingularization of the u…
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…
Second-order mass estimates for static vacuum metrics with small Bartnik data
David Wiygul
Given on the -sphere Bartnik data (prescribed metric and mean curvature) that is a small perturbation of the corresponding data for the standard unit sphere in Euclidean space,…
The Lawson surfaces are determined by their symmetries and topology
Nikolaos Kapouleas, David Wiygul
We prove that a closed embedded minimal surface in the round three-sphere which satisfies the symmetries of a Lawson surface and has the same genus is congruent to the Lawson surfa…
The index and nullity of the Lawson surfaces
Nikolaos Kapouleas, David Wiygul
We prove that the Lawson surface in Lawson's original notation, which has genus and can be viewed as a desingularization of two orthogonal great two-spheres in the ro…
Free-boundary minimal surfaces with connected boundary in the -ball by tripling the equatorial disc
Nicolaos Kapouleas, David Wiygul
In the Euclidean unit three-ball, we construct compact, embedded, two-sided free boundary minimal surfaces with connected boundary and prescribed high genus, by a gluing constructi…
Minimal surfaces in the 3-sphere by desingularizing intersecting Clifford tori
Nikolaos Kapouleas, David Wiygul
For each integer , we apply gluing methods to construct sequences of minimal surfaces embedded in the round -sphere. We produce two types of sequences, all desingulari…
The Bartnik-Bray outer mass of small metric spheres in time-symmetric 3-slices
David Wiygul
Given a sphere with Bartnik data close to that of a round sphere in Euclidean 3-space, we compute its Bartnik-Bray outer mass to first order in the data's deviation from the standa…
Minimal surfaces in the 3-sphere by stacking Clifford tori
David Wiygul
Extending work of Kapouleas and Yang, for any integers , , and sufficiently large, we apply gluing methods to construct in the round -sphere a clos…
Minimal surfaces in the 3-sphere by doubling the Clifford torus over rectangular lattices
David Wiygul
Building on work of Kapouleas and Yang, we construct sequences of minimal surfaces embedded in the round 3-sphere which converge to the Clifford torus counted with multiplicity two…