Annals of Mathematics

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• Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains AI翻译
  作者：Korobkov, Mikhail V.; Pileckas, Konstantin; Russo, Remigio
  摘要：We study the nonhomogeneous boundary value problem for the Navier-Stokes equations of steady motion of a viscous incornpressible fluid in arbitrary bounded multiply connected plane or axially-symmetric spatial domains. (For axially symmetric domains, data is assumed to be axially symmetric as well.) We prove that this problem has a solution under the sole necessary condition of zero total flux through the boundary. The problem was formulated by Jean Leray 80 years ago. The proof of the main re...
• Almost contact 5-manifolds are contact AI翻译
  作者：Casals, Roger; Pancholi, Dishant M.; Presas, Francisco
  摘要：The existence of a contact structure is proved in any homotopy class of almost contact structures on a closed 5-dimensional manifold.
• A relative version of the conjecture of periods of Kontsevich-Zagier AI翻译
  作者：Ayoub, Par Joseph
  摘要：We start with a series F = Sigma(r >>-infinity) f(r) . pi(r) with indeterminate pi and where the coefficients f(r) = fr (z(1),..., z(n)) are holomorphic functions defined on an open neighborhood of the closed polydisc (D) over bar (n) = {( z(1),...,z(n)); | zi | <= 1}. Integrating the coefficients of this series on the n-dimensional real cube [0, 1](n) yields a Laurent series integral(n)([0,1]) F. When F is algebraic we say that integral(n)([0,1]) F is a series of periods. In this article, our...
• Tightness is preserved by Legendrian surgery AI翻译
  作者：Wand, Andy
  摘要：This paper describes a characterization of tightness of closed contact 3-manifolds in terms of supporting open book decompositions. The main result is that tightness of a closed contact 3-manifold is preserved under Legendrian surgery.
• On the Erdos distinct distances problem in the plane AI翻译
  作者：Guth, Larry; Katz, Nets Hawk
  摘要：In this paper, we prove that a set of N points in R-2 has at least cN/log N distinct distances, thus obtaining the sharp exponent in a problem of Erdos. We follow the setup of Elekes and Sharir which, in the spirit of the Erlangen program, allows us to study the problem in the group of rigid motions of the plane. This converts the problem to one of point-line incidences in space. We introduce two new ideas in our proof. In order to control points where many lines are incident, we create a cell...
• Positivity for cluster algebras AI翻译
  作者：Lee, Kyungyong; Schiffler, Ralf
  摘要：We prove the positivity conjecture for all skew-symmetric cluster algebras.
• Regularity of Einstein manifolds and the codimension 4 conjecture AI翻译
  作者：Cheeger, Jeff; Naber, Aaron
  摘要：In this paper, we are concerned with the regularity of noncollapsed Riemannian manifolds (M-n, g) with bounded Ricci curvature, as well as their Gromov-Hausdorff limit spaces (M-j(n), d(j)) ->(dGH) (X, d), where d(j), denotes the Riemannian distance. Our main result is a solution to the codimension 4 conjecture, namely that X is smooth away from a closed subset of codimension 4. We combine this result with the ideas of quantitative stratification to prove a priori L-q estimates on the full cur...
• Anomalous dissipation for 1/5-Holder Euler flows AI翻译
  作者：Buckmaster, Tristan; De Lellis, Camillo; Isett, Philip; Szekelyhidi, Laszlo, Jr.
  摘要：Recently the second and fourth authors developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in Holder spaces. The motivation comes from Onsager's conjecture. The construction involves a superposition of weakly interacting perturbed Beltrami flows on infinitely many scales. An obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field. In a recent paper the third author has impr...
• Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 AI翻译
  作者：Bhargava, Manjul; Shankar, Arul
  摘要：We prove an asymptotic formula for the number of SL3 (Z)-equivalence classes of integral ternary cubic forms having bounded invariants. We use this result to show that the average size of the 3-Selmer group of all elliptic curves, when ordered by height, is equal to 4. This implies that the average rank of all elliptic curves, when ordered by height, is less than 1.17. Combining our counting techniques with a recent result of Dokchitser and Dokchitser, we prove that a positive proportion of al...
• Construction of Cauchy data of vacuum Einstein field equations evolving to black holes AI翻译
  作者：Li, Junbin; Yu, Pin
  摘要：We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant time slice in Minkowski space-time inside and exactly a constant time slice in Kerr space-time outside. The proof makes use of the full strength of Christodoulou's work on the dynamical formation of black holes and Corvino-Schoen's work on the construction of...