Acta Mathematica

最新文章

• Normal subgroups in the Cremona group AI翻译
  作者：Cantat, Serge; Lamy, Stephane; de Cornulier, Yves
  作者单位：Universite de Rennes; University of Warwick; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
  摘要：Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory and algebraic geometry to produce elements in the Cremona group that generate non-trivial normal subgroups.
• 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...
• On the generalized lower bound conjecture for polytopes and spheres AI翻译
  作者：Murai, Satoshi; Nevo, Eran
  作者单位：Yamaguchi University; Ben-Gurion University of the Negev
  摘要：In 1971, McMullen and Walkup posed the following conjecture, which is called the generalized lower bound conjecture: If P is a simplicial d-polytope then its h-vector (h (0), h (1), aEuro broken vertical bar, h (d) ) satisfies . Moreover, if h (r-1) = h (r) for some then P can be triangulated without introducing simplices of dimension a parts per thousand currency signd - r. The first part of the conjecture was solved by Stanley in 1980 using the hard Lefschetz theorem for projective toric var...
• Existence and uniqueness of linking systems: Chermak's proof via obstruction theory AI翻译
  作者：Oliver, Bob
  作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We present a version of a proof by Andy Chermak of the existence and uniqueness of centric linking systems associated with arbitrary saturated fusion systems. This proof differs from the one in [Ch2] in that it is based on the computation of derived functors of certain inverse limits. This leads to a much shorter proof, but one which is aimed mostly at researchers familiar with homological algebra.
• 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.
• Forcing axioms and the continuum hypothesis AI翻译
  作者：Aspero, David; Larson, Paul; Moore, Justin Tatch
  作者单位：University of East Anglia; University System of Ohio; Miami University; Cornell University
  摘要：Woodin has demonstrated that, in the presence of large cardinals, there is a single model of ZFC which is maximal for I (2)-sentences over the structure (H(omega (2)), a, NS (omega 1)), in the sense that its (H(omega (2)), a, NS (omega 1)) satisfies every I (2)-sentence sigma for which (H(omega (2)), a, NS (omega 1)) aS sigma can be forced by set-forcing. In this paper we answer a question of Woodin by showing that there are two I (2)-sentences over the structure (H(omega (2)), a, omega (1)) w...
• 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...
• Invariant Peano curves of expanding Thurston maps AI翻译
  作者：Meyer, Daniel
  作者单位：Constructor University
  摘要：We consider Thurston maps, i.e., branched covering maps f:S (2) -> S (2) that are post-critically finite. In addition, we assume that f is expanding in a suitable sense. It is shown that each sufficiently high iterate F = f (n) of f is semi-conjugate to z (d) :S (1) -> S (1), where d = deg F. More precisely, for such an F we construct a Peano curve gamma:S (1) -> S (2) (onto), such that Fa similar to gamma(z) = gamma(z (d) ) (for all zaS (1)).
• 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...