Annals of Mathematics

最新文章

• Isomonodromy transformations of linear systems of difference equations AI翻译
  作者：Borodin, A
  摘要：We introduce and study isomonodromy transformations of the matrix linear difference equation Y(z + 1) = A(z)Y(z) with polynomial A(z). Our main result is construction of an isomonodromy action of Z(m(n+1)-1) on the space of coefficients A(z) (here m is the size of matrices and n is the degree of A(z)). The (birational) action of certain rank n subgroups can be described by difference analogs of the classical Schlesinger equations, and we prove that for generic initial conditions these differen...
• On a vanishing conjecture appearing in the geometric Langlands correspondence AI翻译
  作者：Gaitsgory, D
• The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks AI翻译
  作者：Colding, TH; Minicozzi, WP
• Extension properties of meromorphic mappings with values in non-Kahler complex manifolds AI翻译
  作者：Ivashkovich, S
• Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers AI翻译
  作者：Morales, CA; Pacifico, MJ; Pujals, ER
  摘要：Inspired by Lorenz' remarkable chaotic flow, we describe in this paper the structure of all C-1 robust transitive sets with singularities for flows on closed 3-manifolds: they are partially hyperbolic with volume-expanding central direction, and are either attractors or repellers. In particular, any C-1 robust attractor with singularities for flows on closed 3-manifolds always has an invariant foliation whose leaves are forward contracted by the flow, and has positive Lyapunov exponent at ever...
• Determination of the algebraic relations among special Γ-values in positive characteristic AI翻译
  作者：Anderson, GW; Brownawell, WD; Papanikolas, MA
  摘要：We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric Gamma-function over F-q[T] are explained by the standard functional equations.
• The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks AI翻译
  作者：Colding, TH; Minicozzi, WP
• Semistable sheaves in positive characteristic AI翻译
  作者：Langer, A
  摘要：We prove Maruyama's conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring. Our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field. This result implies that in mixed characteristic the moduli spaces of Gieseker semistable sheaves are projective schemes of finite type. The proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slop...
• Positive extensions, Fejer-Riesz factorization and autoregressive filters in two variables AI翻译
  作者：Geronimo, JS; Woerdeman, HJ
  摘要：In this paper we treat the two-variable positive extension problem for trigonometric polynomials where the extension is required to be the reciprocal of the absolute value squared of a stable polynomial. This problem may also be interpreted as an autoregressive filter design problem for bivariate stochastic processes. We show that the existence of a solution is equivalent to solving a finite positive definite matrix completion problem where the completion is required to satisfy an additional l...
• The subconvexity problem for Rankin-Selberg L-functions and equidistribution of Heegner points AI翻译
  作者：Michel, P
  摘要：In this paper we solve the subconvexity problem for Rankin-Selberg L-functions L(f circle times g, s) where f and g are two cuspidal automorphic forms over Q, g being fixed and f having large level and nontrivial nebentypus. We use this subconvexity bound to prove an equidistribution property for incomplete orbits of Heegner points over definite Shimura curves.