The convexity of a planar domain via properties of solutions to the modified Helmholtz equation
Nikolay Kuznetsov
Abstract
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 respect to the domain's boundary via real-valued solutions of the modified Helmholtz equation, and the convexity of a planar domain in which the distance function is superharmonic