2期

最新文章

• Extension theorems, non-vanishing and the existence of good minimal models AI翻译
  作者：Demailly, Jean-Pierre; Hacon, Christopher D.; Paun, Mihai
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Utah System of Higher Education; University of Utah; Universite de Lorraine
  摘要：We prove an extension theorem for effective purely log-terminal pairs (X, S + B) of non-negative Kodaira dimension . The main new ingredient is a refinement of the Ohsawa-Takegoshi L (2) extension theorem involving singular Hermitian metrics.
• p-adic logarithmic forms and a problem of Erdos AI翻译
  作者：Yu, Kunrui
  作者单位：Hong Kong University of Science & Technology
  摘要：For any natural number m(> 1) let P(m) denote the greatest prime divisor of m. By the problem of ErdAs in the title of the present paper we mean the general version of his problem, that is, his conjecture from 1965 that (see ErdAs [10]) and its far-reaching generalization to Lucas and Lehmer numbers. In the present paper the author delivers three refinements upon Yu [40] required by C. L. Stewart for solving completely the problem of ErdAs (see Stewart [25]). The author gives also some remarks...
• The energy density in the planar Ising model AI翻译
  作者：Hongler, Clement; Smirnov, Stanislav
  作者单位：Columbia University; University of Geneva; Saint Petersburg State University
  摘要：We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a discrete fermionic correlator and compute its scaling limit by discrete complex analysis methods. As a consequence, we obtain a simple exact formula for the scaling limit of the energy field one-point function in terms of the hyperbolic metric. This confirms the predictions originating in physics, but also provides a hig...
• Embedded minimal tori in S 3 and the Lawson conjecture AI翻译
  作者：Brendle, Simon
  作者单位：Stanford University
  摘要：We show that any embedded minimal torus in S (3) is congruent to the Clifford torus. This answers a question posed by H. B. Lawson, Jr., in 1970.
• Uniqueness of non-linear ground states for fractional Laplacians in AI翻译
  作者：Frank, Rupert L.; Lenzmann, Enno
  作者单位：Princeton University; University of Copenhagen
  摘要：We prove uniqueness of ground state solutions Q = Q(vertical bar x vertical bar) >= 0 of the non-linear equation (-Delta)(s)Q+Q-Q(alpha+1)=0 in R, (-Delta) s Q + Q - Q alpha + 1 = 0 in R, where 0 < s < 1 and 0 < alpha < 4s/(1-2s) for s<1/2 s<1 2 and 0 < alpha < infinity for s >= 1/2 s >= 1 2. Here (-Delta)(s) denotes the fractional Laplacian in one dimension. In particular, we answer affirmatively an open question recently raised by Kenig-Martel-Robbiano and we generalize (by completely differ...
• The Brownian map is the scaling limit of uniform random plane quadrangulations AI翻译
  作者：Miermont, Gregory
  作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：We prove that uniform random quadrangulations of the sphere with n faces, endowed with the usual graph distance and renormalized by n (-1/4), converge as n -> a in distribution for the Gromov-Hausdorff topology to a limiting metric space. We validate a conjecture by Le Gall, by showing that the limit is (up to a scale constant) the so-called Brownian map, which was introduced by Marckert-Mokkadem and Le Gall as the most natural candidate for the scaling limit of many models of random plane map...
• Proof of the BMV conjecture AI翻译
  作者：Stahl, Herbert R.
  摘要：We prove the BMV (Bessis, Moussa, Villani, [1]) conjecture, which states that the function , , is the Laplace transform of a positive measure on [0,a) if A and B are Hermitian matrices and B is positive semidefinite. A semi-explicit representation for this measure is given.
• On divisors of Lucas and Lehmer numbers AI翻译
  作者：Stewart, Cameron L.
  作者单位：University of Waterloo
  摘要：Let u (n) be the nth term of a Lucas sequence or a Lehmer sequence. In this article we shall establish an estimate from below for the greatest prime factor of u (n) which is of the form n exp(log n/104 log log n). In doing so, we are able to resolve a question of Schinzel from 1962 and a conjecture of ErdAs from 1965. In addition we are able to give the first general improvement on results of Bang from 1886 and Carmichael from 1912.
• Isotropy of unitary involutions AI翻译
  作者：Karpenko, Nikita; Zhykhovich, Maksim
  作者单位：University of Alberta; Johannes Gutenberg University of Mainz
  摘要：We prove the so-called unitary isotropy theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal, symplectic, and unitary involutions are formal consequences of this theorem. A component of the proof is a detailed study of the quasi-split unitary grassmannians.