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• A geometric approach to complete reducibility AI翻译
  作者：Bate, M; Martin, B; Röhrle, G
  作者单位：University of Birmingham; University of Canterbury
  摘要：Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert-Mumford-Kempf from geometric invariant theory. We deduce that a normal subgroup of a G-completely reducible subgroup of G is again G-completely reducible, ...
• A strongly aperiodic set of tiles in the hyperbolic plane AI翻译
  作者：Goodman-Strauss, C
  作者单位：University of Arkansas System; University of Arkansas Fayetteville
  摘要：We construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane. Such a set of tiles does admit a tiling, but admits no tiling with an infinite cyclic symmetry. This can also be regarded as a regular production system [5] that does admit bi-infinite orbits, but admits no periodic orbits.
• On the effective Nullstellensatz AI翻译
  作者：Jelonek, Z
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
  摘要：Let K be an algebraically closed field and let X subset of K-m be an n-dimensional affine variety. Assume that f(1),..., f(k) are polynomials which have no common zeros on X. We estimate the degrees of polynomials A(i) is an element of K[X] such that 1 = Sigma(k)(i=1) A(i) f(i) n X. Our estimate is sharp for k <= n and nearly sharp for k > n. Now assume that f(1),..., f(k) are polynomials on X. Let I = (f(1),..., f(k)). K[X] be the ideal generated by fi. It is well-known that there is a number...
• On uniform exponential growth for linear groups AI翻译
  作者：Eskin, A; Mozes, S; Oh, H
  作者单位：University of Chicago; Hebrew University of Jerusalem; Princeton University; Institute for Advanced Study - USA
• Bilinear eigenfunction estimates and the nonlinear Schrodinger equation on surfaces AI翻译
  作者：Burq, N; Gérard, P; Tzvetkov, N
  作者单位：Universite Paris Saclay
  摘要：We study the cubic non linear Schrodinger equation (NLS) on compact surfaces. On the sphere S-2 and more generally on Zoll surfaces, we prove that, for s > 1/4, NLS is uniformly well-posed in H-s, which is sharp on the sphere. The main ingredient in our proof is a sharp bilinear estimate for Laplace spectral projectors on compact surfaces.
• Perverse sheaves on real loop Grassmannians AI翻译
  作者：Nadler, D
  作者单位：University of Chicago
  摘要：The aim of this paper is to identify a certain tensor category of perverse sheaves on the loop Grassmannian Gr(R) of a real form G(R) of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a connected reductive complex algebraic subgroup H of the dual group. G. The root system of H is closely related to the restricted root system of G(R). The fact that H is reductive implies that an interesting family of real algebraic maps satisfies the c...
• The nilpotence conjecture in K-theory of toric varieties AI翻译
  作者：Gubeladze, J
  作者单位：California State University System; San Francisco State University
  摘要：It is shown that all nontrivial elements in higher K-groups of toric varieties are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties.
• Infinitesimal form boundedness and Trudinger's subordination for the Schrodinger operator AI翻译
  作者：Maz'ya, VG; Verbitsky, IE
  作者单位：University System of Ohio; Ohio State University; University of Liverpool; University of Missouri System; University of Missouri Columbia
  摘要：We give explicit analytic criteria for two problems associated with the Schrodinger operator H = -Delta + Q on L-2(R-n) where Q is an element of D'(R-n) is an arbitrary real- or complex-valued potential. First, we obtain necessary and sufficient conditions on Q so that the quadratic form < Q(.), (.)> has zero relative bound with respect to the Laplacian. For Q is an element of L-loc(1)(R-n), this property can be expressed in the form of the integral inequality: vertical bar integral(Rn) vertic...
• On the stability of Riemannian manifold with parallel spinors AI翻译
  作者：Dai, XZ; Wang, XD; Wei, GF
  作者单位：University of California System; University of California Santa Barbara; Massachusetts Institute of Technology (MIT)
  摘要：Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric wi...
• Kupka-Smale theorem for polynomial automorphisms of C2 and persistence of heteroclinic intersections AI翻译
  作者：Buzzard, GT; Hruska, SL; Ilyashenko, Y
  作者单位：Purdue University System; Purdue University; Cornell University; Lomonosov Moscow State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
  摘要：A map is Kupka-Smale if all periodic points are hyperbolic and the stable and unstable manifolds of any two saddle points are transverse. Here we prove that Kupka-Smale maps form a residual set of full Lebesgue measure in the space P-d of polynomial automorphisms of C-2 of fixed dynamical degree d >= 2. We also prove that a heteroclinic point of two saddle periodic orbits may be continued over (almost) the entire parameter space for this set of maps. This is one of the first persistence theore...