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In 1970, Kobayashi conjectured that general hypersurfaces of sufficiently large degree in
are hyperbolic. In this paper we prove that a general sufficiently ample hypersurface in a smooth projective variety is hyperbolic. To prove this statement, we construct...
A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently obtained by the second and third named authors. In this...
be a complex projective variety with only canonical singularities and with trivial canonical bundle. Let
be an ample line bundle on
. Assume that the pair
is the flat limit of a family of smooth polarized Calabi-Yau manifolds. Assume...
We prove a Russo-Seymour-Welsh percolation theorem for nodal domains and nodal lines associated to a natural infinite dimensional space of real analytic functions on the real plane. More precisely, let
be a smooth connected bounded open set in
We present the min-max construction of critical points of the area using penalization arguments. Precisely, for any immersion of a closed surface
into a given closed manifold, we add to the area Lagrangian a term equal to the
norm of the second fundamental...
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