Metric and variational structures in singular varieties
The aim is to bring together mathematicians belonging to two communities: those working on quantitative aspects of subanalytic geometry and those working on geometric measure theory as it relates to subanalytic geometry.
Here are some examples: The Lojasiewicz inequality has an innite dimensional version and constitutes a main step in Simon's proof of the uniqueness of the tangent cone to a stationary varifold (generalized minimal surface of arbitrary dimension and codimension in
Euclidean space) at an isolated singular point. The rate of convergence, predicted
by the proof, of homethetic expansions of the stationary varifold to its tangent cone
is slower than "geometric", and shown by examples to be optimal. It is the same
rate of convergence obtained in Kurdyka-Mostowski-Parusinski's proof of the Thom
gradient conjecture: the secants to the integral curves of an analytic vector eld
vanishing at one point converge to a unique limit.