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math.DG2024
Witten instanton complex and Morse-Bott inequalities on stratified pseudomanifolds
Gayana Jayasinghe, Hadrian Quan, Xinran Yu
In this paper we construct Witten instanton complexes on stratified pseudomanifolds with wedge metrics, for all choices of mezzo-perversities which classify the self-adjoint extens…
math.DG2023
Self-adjointness criteria and self-adjoint extensions of the Laplace-Beltrami operator on -Grushin manifolds
Ivan Beschastnyi, Hadrian Quan
The Grushin plane serves as one of the simplest examples of a sub-Riemannian manifold whose distribution is of non-constant rank. Despite the fact that the singular set where this…
math.DG2019★ 2 cited
Sub-Riemannian limit of the differential form heat kernels of contact manifolds
Pierre Albin, Hadrian Quan
We study the behavior of the heat kernel of the Hodge Laplacian on a contact manifold endowed with a family of Riemannian metrics that blow-up the directions transverse to the cont…