查看更多>>摘要：In this paper,we study the theory of complements,introduced by Shokurov,for Calabi-Yau type varieties with the coefficient set[0,1].We show that there exists a finite set of positive integers N,such that if a threefold pair(X/Z ∋ z,B)has an R-complement which is klt over a neighborhood of z,then it has an n-complement for some n ∈ N.We also show the boundedness of complements for R-complementary surface pairs.
查看更多>>摘要：We study the three-dimensional many-particle quantum dynamics in mean-field set-ting.We forge together the hierarchy method and the modulated energy method.We prove rigorously that the compressible Euler equation is the limit as the particle num-ber tends to infinity and the Planck's constant tends to zero.We improve the previous sufficient small time hierarchy argument to any finite time via a new iteration scheme and Strichartz bounds first raised by Klainerman and Machedon in this context.We establish strong and quantitative microscopic to macroscopic convergence of mass and momentum densities up to the 1st blow up time of the limiting Euler equation.We justify that the macroscopic pressure emerges from the space-time averages of micro-scopic interactions via the Strichartz-type bounds.We have hence found a physical meaning for Strichartz-type bounds.
查看更多>>摘要：In this article,we present characterizations of the concavity property of minimal L2 integrals degenerating to linearity in the case of products of analytic subsets on products of open Riemann surfaces.As applications,we obtain characterizations of the holding of equality in optimal jets L2 extension problem from products of analytic subsets to products of open Riemann surfaces,which implies characterizations of the product versions of the equality parts of Suita conjecture and extended Suita conjecture,and the equality holding of a conjecture of Ohsawa for products of open Riemann surfaces.
查看更多>>摘要：We prove Lp bounds for the Fourier extension operators associated to smooth surfaces in R3 with negative Gaussian curvatures for every p＞3.25.
查看更多>>摘要：We prove that if the frequency of the quasi-periodic SL(2,R)cocycle is Diophantine,then each of the following properties is dense in the subcritical regime:for any 1/2＜κ＜1,the Lyapunov exponent is exactly κ-Hölder continuous;the extended eigenstates of the potential have optimal sub-linear growth;and the dual operator associated with a subcritical potential has power-law decaying eigenfunctions.The proof is based on fibered Anosov-Katok constructions for quasi-periodic SL(2,R)cocycles.
查看更多>>摘要：We formulate a local analogue of the ghost conjecture of Bergdall and Pollack,which essentially relies purely on the representation theory of GL2(Qp).We further study the combinatorial properties of the ghost series as well as its Newton polygon,in particular,giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes.In a forthcoming sequel,we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications.
查看更多>>摘要：We introduce an algebraicity criterion.It has the following form:Consider an analytic subvariety of some algebraic variety X over a global field K.Under certain conditions,if X contains manyK-points,then X is algebraic over K.This gives a way to show the transcendence of points via the transcendence of analytic subvarieties.Such a situ-ation often appears when we have a dynamical system,because we can often produce infinitely many points from one point via iterates.Combining this criterion and the study of invariant subvarieties,we get some results on the transcendence in arithmetic dynamics.We get a characterization for products of Böttcher coordinates or products of multiplicative canonical heights for polynomial dynamical pairs to be algebraic.For this,we study the invariant subvarieties for products of endomorphisms.In particular,we partially generalize Medvedev-Scanlon's classification of invariant subvarieties of split polynomial maps to separable endomorphisms on(Pl)N in any characteristic.We also get some high dimensional partial generalization via introducing a notion of independence.We then study dominant endomorphisms f on AN over a number field of algebraic degree d ≥ 2.We show that in most cases(e.g.when such an endomor-phism extends to an endomorphism on PN),there are many analytic curves centered at infinity which are periodic.We show that for most of them,it is algebraic if and only if it contains at least one algebraic point.We also study the periodic curves.We show that for most f,all periodic curves have degree at most 2.When N=2,we get a more precise classification result.We show that under a condition which is satisfied for a general f,if f has infinitely many periodic curves,then f is homogenous up to change of origin.
查看更多>>摘要：We study the convergence rate of Bergman metrics on the class of polarized pointed Kähler n-manifolds(M,L,g,x)with Vol(B1(x))＞v and |sec| ≤ K on M.Relying on Tian's peak section method(Tian in J Differ Geom 32(1):99-130,1990),we show that the C1,α convergence of Bergman metrics is uniform.In the end,we discuss the sharpness of our estimates.
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