Showing papers in "Advances in Mathematics in 2014"

TL;DR: In this paper, a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac-Moody algebras is developed.

TL;DR: In this paper, a weak version of the quantum de Finetti theorem is used to prove the validity of Hartree's theory for the ground state energy of bosonic quantum systems in the mean-field regime.

TL;DR: In this article, the authors solved the logarithmic Minkowski problem for the case of discrete Borel measures whose supports are in general position, and solved the problem for even Borel measure.

TL;DR: In this article, the structure of a Poisson manifold with Poisson bivector field Π is studied and a variant of de Rham theory for these manifolds and its connection with poisson cohomology is investigated.

TL;DR: In this article, the geometry of folding paths in outer space was developed and it was shown that the complex of free factors of a free group of finite rank is hyperbolic.

TL;DR: In this paper, it was shown that L 2 (μ) has an exponential orthonormal basis if and only if ρ = 1 q for some q > 0 and N divides q.

TL;DR: In this paper, it was shown that the Nakayama automorphism of a skew Calabi-Yau algebra has a trivial homological determinant in case A is noetherian, connected graded, and Koszul.

TL;DR: In this paper, the Orlicz addition of convex bodies containing the origin in their interiors was introduced, and the L p Minkowski mixed volume inequality was extended to the ORlicz mixed volume inequalities by using the ORICZ Brunn-Minkowski inequality.

TL;DR: In this article, it was shown that the Bohr radius of the polydisk D^n behaves asymptotically as ω(log n)/n, where n is the number of vertices in the disk.

TL;DR: In this article, the authors established quantitative estimates for solutions u ( t, x ) to the fractional nonlinear diffusion equation, ∂ t u + ( − Δ ) s ( u m ) = 0 in the whole range of exponents m > 0, 0 s 1.

TL;DR: In this article, the Fourier transform is applied to acyclic graded quiver varieties to obtain deformed monoidal categorifications of quantum quantum cluster algebras with specific coefficients.

TL;DR: In this article, it was shown that the diameter of the d-dimensional associahedron is 2 d − 4 when d is greater than 9 and that the maximally distant vertices of this polytope are explicitly described as triangulations of a convex polygon.

TL;DR: In this paper, a trigonal curve with three infinite points and two algebraic functions carrying the data of the divisor is introduced, and the asymptotic properties of the Baker-Akhiezer function and the two functions are studied near the trigonal curves.

TL;DR: In this article, a dual Orlicz-Brunn-Minkowski theory is presented, and the equivalence between the dual ORlicz and Minkowski inequality is demonstrated.

TL;DR: In this article, it was shown that k-th order derivatives of perturbative classical solutions to the hard and soft potential Boltzmann equation (without the angular cut-off assumption) converge in large time to the global Maxwellian with the optimal decay rate of O( t − 1 2 (k + ϱ + n 2 − n r ) ) in the L x r (L v 2 ) -norm for any 2 ≤ r ≤ ∞.

TL;DR: In this paper, Liouville-type and partial regularity results for the nonlinear fourth-order problem were derived for both Lioupville-and partial-regularity results.

TL;DR: In this article, various models for singularity categories of modules over differential graded rings were constructed based on the connection between abelian model structures, cotorsion pairs and deconstructible classes.

TL;DR: In this article, the Bochner-Weitzenbock formula for the Laplacian on general Finsler manifolds was proved and Li-Yau type gradient estimates as well as parabolic Harnack inequalities were derived.

TL;DR: The Orlicz-John ellipsoid as discussed by the authors is a generalization of the classical John ellipseid and the evolved L p John ellipssoid, and the analog of Ball's volume-ratio inequality is established for the new ORlicz -John ellipsse.

TL;DR: In this article, the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces were studied via the direct method of calculus of variations.

TL;DR: In this paper, the authors discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W -algebras and vertex algesbras in general and formulate a Verlinde-type formula for the fusion rules of irreducible W 2, 2 p − 1 ) -modules.

TL;DR: In this article, it was shown that if a measure has an associated frame measure, then it must have a certain uniformity in the sense that the weight is distributed quite uniformly on its support.

TL;DR: In this article, it was shown that if A arises as an H-module algebra via an inner faithful H-action, then H must be a group algebra, and the main results of this paper extend to working over k of positive characteristic.

TL;DR: In this paper, the low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data is rigorously justified in the whole space R 3, where the uniform estimates of the solutions in a Sobolev space are established on a finite time interval independent of the Mach number.

TL;DR: In this article, a new class of finite dimensional algebras of global dimension n, called n-representation infinite, is introduced, which is a certain analog of representation infinite hereditary algesbras, and three important classes of modules are studied: n-preprojective, n-prior and n-regular modules.

TL;DR: In this paper, the cone volume measure of a polytope with centroid at the origin is proved to satisfy the subspace concentration condition, and a conjectured sharp affine isoperimetric inequality for the U-functional is completely established.

TL;DR: A new counting lemma is proved following the functional approach of Gowers, which complements the sparse regularity lemma of Kohayakawa and Rodl, allowing us to count small graphs in regular subgraphs of a sufficiently pseudorandom graph and to prove sparse extensions of several well-known combinatorial theorems.

TL;DR: In this article, the inverse curvature flow was used to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.

TL;DR: In this paper, a weighted norm inequality of Muckenhoupt-Wheeden type is obtained for gradients of solutions to a class of quasilinear Riccati type equations with measure data on Reifenberg flat domains.

TL;DR: In this article, the quermassintegrals and the curvature integrals in the hyperbolic space H n were solved by using quermasso-integral preserving curvature flows.