Showing papers in "Advances in Mathematics in 2011"

TL;DR: In this paper, the connection between the fractional Laplacian operator and a class of conformally covariant operators in conformal geometry was studied, and the connections between Caffarelli and Silvestre were established.

TL;DR: In this article, the authors consider the eigenvalues and eigenvectors of finite, low-rank perturbations of random matrices and uncover a phase transition phenomenon whereby the large matrix limit of the extreme eigen values of the perturbed matrix differs from that of the original matrix if and only if the eigvalues of the matrix are above a certain critical threshold.

TL;DR: In this article, the global existence, conditional regularity and uniqueness of a weak solution for the 2D MHD equations with only magnetic diffusion were established for mixed partial dissipation and magnetic diffusion.

TL;DR: In this article, the authors consider the relationship of the geometry of compact Riemannian manifolds with boundary to the first nonzero eigenvalue σ 1 of the Dirichlet-to-Neumann map (Steklov eigen value).

TL;DR: Weakly group-theoretical fusion categories have been shown to be solvable in this article, which is a categorical analog of Burnside's theorem for finite groups and has powerful applications to fusion categories and semisimple Hopf algebras of a given dimension.

TL;DR: In this article, a theory of slice regular functions on a real alternative algebra A is developed based on a well-known Fueter's construction, which permits to extend the range of these function theories and to obtain new results, including a strong form of the fundamental theorem of algebra for an ample class of polynomials with coefficients in A and a Cauchy integral formula for slice functions of class C 1.

TL;DR: In this paper, it was shown that Derksen-Weyman-Zelevinsky's mutations of quivers with potential yield equivalences of suitable 3-Calabi-Yau triangulated categories can be derived.

TL;DR: In this article, the Laurent expansion of any cluster variable in any cluster algebra coming from a triangulated surface (with or without punctures), with respect to an arbitrary seed, is studied.

TL;DR: In this article, a theory of existence, uniqueness and regularity for the following porous medium equation with fractional diffusion was developed, and the continuous dependence on data and exponent was established.

TL;DR: In this paper, it was shown that the Auslander-Reiten translation functor τ n plays an important role in the study of n-cluster tilting subcategories.

TL;DR: In this paper, it was shown that the cluster algebra obtained from C [ N w ] by formally inverting the generators of the coefficient ring is isomorphic to the algebra C [ n w ] of regular functions on the unipotent cell N w of the Kac-Moody group with Lie algebra g.

TL;DR: In this article, the L p ( w ) norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the A p characteristic of w for all 1 p ∞.

TL;DR: In this article, the authors studied discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones, and proved uniform convergence of discrete harmonic measures, Greenʼs functions and Poisson kernels to their continuous counterparts.

TL;DR: The c-generalized associahedron as discussed by the authors is a simple polytope whose outer normal fan is a coarsening of the Coxeter fan arising from the Tamari lattice.

TL;DR: In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces B ˙ p, q s and Triebel-Lizorkin spaces F ˚ p, q s for all s ∈ ( 0, 1 ) and p, Q ∈ n / ( n + s ), ∞ ], both in R n and in the metric measure spaces enjoying the doubling and reverse doubling properties.

TL;DR: Hopf monads generalize Hopf algebras to the non-braided setting in this article, and the notion of Hopf adjunctions can be formulated as a bimodal adjunction with an invertibility condition.

TL;DR: In this paper, divergence form elliptic operators of the form (L=-\dv A(x)nabla), defined in Rn+1 + 1 = \{(x,t) ∈ Rn \times R \}, were considered.

TL;DR: In this paper, the moduli spaces of tropical curves and tropical principally polarized abelian varieties are constructed in the category of stacky fans, and the tropical Torelli map between these two modulus spaces is defined.

TL;DR: In this paper, an infinite dimensional KAM theorem was proved for the Schrodinger equation with periodic boundary conditions and a Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system was obtained.

TL;DR: In this article, the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data was studied.

TL;DR: In this paper, it was shown that linear perturbations of a Schwarzschild black hole fall off as $t^{-2\ell-2}$ for general data in the form of weighted $L 1$ to $L ∞$ bounds for solutions of the Regge-Wheeler equation.

TL;DR: The main goal of as discussed by the authors is to prove that the idempotent completions of triangulated categories of singularities of two schemes are equivalent if the formal completions along singularities are isomorphic.

TL;DR: In this paper, it was shown that any real zero polynomial admits a determinantal representation with symmetric matrices, and that no power of it admits a deterministic representation.

TL;DR: In this paper, the authors used the combinatorics of alcove walks to give uniform combinatorial formulas for Macdonald polynomials for all Lie types, including the Weyl character in terms of the Littelmann path model.

TL;DR: In this paper, the space of Minkowski valuations on an m-dimensional complex vector space which are continuous, translation invariant and contravariant under the complex special linear group is explicitly described.

TL;DR: In this article, the authors developed the nonlocal maximum principle introduced in Kiselev, Nazarov and Volberg (2007) for active scalar equations and applied it to finite time regularization of weak solutions in the supercritical regime.

TL;DR: In this paper, the equivariant quantum differential equation for the cotangent bundle T ⁎ B with the affine Knizhnik-Zamolodchikov connection of Cherednik and Matsuo was identified.

TL;DR: In this article, Liouville type theorems for positive entire solutions for I u + u p ⩽ 0, p > 1 were established for a class of nonlinear integral operators.