Intends to prove a Harnack inequality for level sets of $p$-Laplace phase transition minimizers, in particular if a level set is included in a flat cylinder, then, in the interior, it is included in a flatter one.

Presents a study of Wave Maps from $^{2+1}$ to the hyperbolic plane $^$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some $H^{1+mu}$, $mu>0$.

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Proves that the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fus

Introduces a geometric mechanism for diffusion in a priori unstable nearly integrable dynamical systems. This book states that resonances besides destroying the primary KAM tori, create secondary tori and tori of lower dimension.

Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional ri

Studies the elastic problems on simply connected manifolds $M_n$ whose orthonormal frame bundle is a Lie group $G$. This title synthesizes ideas from optimal control theory, adapted to variational problems on the principal bundles of Riemannian spaces, and