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math.AP2024
The convexity of a planar domain via properties of solutions to the modified Helmholtz equation
Nikolay Kuznetsov
A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respe…
math.AP2023
Sloshing in containers with vertical walls: isoperimetric inequalities for the fundamental eigenvalue
Nikolay Kuznetsov
One isoperimetric inequality for the fundamental sloshing eigenvalue is derived under the assumption that containers have vertical side walls and either finite or infinite depth. I…