Inventiones mathematicae

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• Derivative complex, BGG correspondence, and numerical inequalities for compact Kahler manifolds AI翻译
  作者：Lazarsfeld, Robert; Popa, Mihnea
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Michigan System; University of Michigan
• Well-posedness of the transport equation by stochastic perturbation AI翻译
  作者：Flandoli, F.; Gubinelli, M.; Priola, E.
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; University of Pisa; University of Turin
  摘要：We consider the linear transport equation with a globally Holder continuous and bounded vector field, with an integrability condition on the divergence. While uniqueness may fail for the deterministic PDE, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. This seems to be the first explicit example of a PDE of fluid dynamics that becomes well-posed under the influence of a (multiplicative) noise. The key tool is a differentiabl...
• Collapsing irreducible 3-manifolds with nontrivial fundamental group AI翻译
  作者：Bessieres, L.; Besson, G.; Boileau, M.; Maillot, S.; Porti, J.
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Montpellier; Autonomous University of Barcelona
  摘要：Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics which volume-collapses and whose sectional curvature is locally controlled, then M is a graph manifold. This is the last step in Perelman's proof of Thurston's Geometrisation Conjecture.
• Algebraic volume density property of affine algebraic manifolds AI翻译
  作者：Kaliman, Shulim; Kutzschebauch, Frank
  作者单位：University of Miami; University of Bern
  摘要：We introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it, in particular that it implies the volume density property. The main results of the paper are producing two big classes of examples of Stein manifolds with volume density property. One class consists of certain affine modifications of a, (n) equipped with a canonical volume form, the other is the class of all Linear Algebraic Groups equipped with the left in...
• Stability of symplectic leaves AI翻译
  作者：Crainic, Marius; Fernandes, Rui Loja
  作者单位：Universidade de Lisboa; Utrecht University
  摘要：We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not only extends but also provides a new approach (and proofs) to the classical stability results for foliations and group actions.
• A complete characterization of coefficients of a.e. convergent orthogonal series and majorizing measures AI翻译
  作者：Paszkiewicz, Adam
  作者单位：University of Lodz
  摘要：We characterize sequences of numbers (a (n) ) such that a (na parts per thousand yen1) a (n) I broken vertical bar (n) converges a.e. for any orthonormal system (I broken vertical bar (n) ) in any L (2)-space. In our criteria we use the set A={a (ma parts per thousand yenn|)|a (m) |(2);na parts per thousand yen1}, majorizing measures on A, and new descriptions of the complexity of A.
• Affine linear sieve, expanders, and sum-product AI翻译
  作者：Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
  作者单位：Princeton University; University of California System; University of California Santa Cruz; Institute for Advanced Study - USA
  摘要：Let O be an orbit in Z(n) of a finitely generated subgroup Lambda of GL (n) (Z) whose Zariski closure Zcl(Lambda) is suitably large (e.g. isomorphic to SL2). We develop a Brun combinatorial sieve for estimating the number of points on O at which a fixed integral polynomial is prime or has few prime factors, and discuss applications to classical problems, including Pythagorean triangles and integral Apollonian packings. A fundamental role is played by the expansion property of the congruence gr...
• Fake projective planes (vol 168, pg 321, 2007) AI翻译
  作者：Prasad, Gopal; Yeung, Sai-Kee
  作者单位：University of Michigan System; University of Michigan; Purdue University System; Purdue University
• Growth of balls of holomorphic sections and energy at equilibrium AI翻译
  作者：Berman, Robert; Boucksom, Sebastien
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
  摘要：Let L be a big line bundle on a compact complex manifold X. Given a non-pluripolar compact subset K of X and a continuous Hermitian metric e (-phi) on L, we define the energy at equilibrium of (K,phi) as the Monge-AmpSre energy of the extremal psh weight associated to (K,phi). We prove the differentiability of the energy at equilibrium with respect to phi, and we show that this energy describes the asymptotic behaviour as k -> a of the volume of the sup-norm unit ball induced by (K,k phi) on t...
• Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space AI翻译
  作者：Bauer, I.; Catanese, F.
  作者单位：University of Bayreuth