1 citations · 1 across the 6 of their papers we have counts for
7 papers
Prescribed Singular Sets for Z/2-Harmonic 1-Forms on R^n
Jiahuang Chen, Siqi He, Willem Adriaan Salm
Z/2 harmonic 1-forms arise naturally as singular limits in gauge theory and calibrated geometry, but the topology that can occur in their singular sets is poorly understood. In thi…
Deformation rigidity for Z/2 eigensections
Andriy Haydys, Siqi He, Willem Adriaan Salm
We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More pre…
Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms
Siqi He, Willem Adriaan Salm
We study metric perturbations and deformation theory for degenerate Z/2-harmonic 1-forms. For a natural class of degenerate examples, we prove that after a suitable perturbation of…
Search for Z/2 eigenfunctions on the sphere using machine learning
Andriy Haydys, Willem Adriaan Salm
We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we impleme…
A stabilization result for Z/2-harmonic 1-forms by constructing solutions on closed 3-manifolds with long cylindrical necks
Willem Adriaan Salm
In this paper, we give an explicit construction of families of -harmonic 1-forms that degenerate to manifolds with cylindrical ends. We do this by considering certain…
Elliptic analysis on collapsing gravitational instantons modelled using the Gibbons-Hawking ansatz
Willem Adriaan Salm
In this paper, we will establish elliptic regularity estimates on families of gravitational instantons whose model metric near infinity collapse to a flat 3 dimensional space. We s…
Construction of gravitational instantons with non-maximal volume growth via codimension-1 collapse
Willem Adriaan Salm
In this paper, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH* using a gluing construction. Away from a finite set of exceptional points, the metr…