  We study the survival probability of a particle diffusing in a
two-dimensional domain, bounded by a smooth absorbing boundary. The short-time
expansion of this quantity depends on the geometric characteristics of the
boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue
of the Dirichlet Laplacian defined on the domain. We present a simple algorithm
for calculation of the short-time expansion for an arbitrary "star-shaped"
domain. The coefficients are expressed in terms of powers of boundary
curvature, integrated around the circumference of the domain. Based on this
expansion, we look for a Pad\'e interpolation between the short-time and the
long-time behavior of the survival probability, i.e. between geometric
characteristics of the boundary and the lowest eigenvalue of the Dirichlet
Laplacian.
