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math.AP2024
On the three-dimensional shape of a crystal
Emanuel Indrei, Aram Karakhanyan
In this paper we completely settle the Almgren problem in under some generic conditions on the potential and tension functions. The problem, among other things, appea…
math.AP2024
Stable cones in the Alt-Phillips free boundary problem
Aram Karakhanyan, Tomás Sanz-Perela
In this paper we prove a classification result for axially symmetric one phase minimizers of the Alt-Phillips free boundary problem in dimensions 3, 4, and 5. To accomplish this, w…
math.AP2024
The Dirichlet-Neumann Operator for Taylor's Cone
Yucong Huang, Aram Karakhanyan
The aim of this paper is to analyse the Dirichlet-Neumann operator in axially symmetric conical domains. We provide a constructive treatment of the generic singularity at the verte…