The Convexity of a Planar Domain Via Properties of Solutions to the Modified Helmholtz Equation
摘要
A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan formula expressing the distance function with respect to the boundary of a domain in terms of real-valued solutions to the modified Helmholtz equation and the convexity of a planar domain where the distance function is superharmonic.