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作者：Dang, Nguyen-Bac; Favre, Charles
摘要：We prove that dynamical degrees of rational self-maps on projective varieties can be interpreted as spectral radii of naturally defined operators on suitable Banach spaces. Generalizing Shokurov's notion of b-divisors, we consider the space of b-classes of higher codimension cycles, and endow this space with various Banach norms. Building on these constructions, we design a natural extension to higher dimensions of the Picard-Manin space introduced by Cantat and Boucksom-Favre-Jonsson in the c...
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作者：Dac, Tuan Ngo
摘要：We study Todd-Thakur's analogues of Zagier-Hoffman's conjectures in positive characteristic. These conjectures predict the dimension and an explicit basis J(w) of the span of characteristic p multiple zeta values of fixed weight w which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In the present paper we first establish the algebraic part of these conjectures which states that the span of characteristic p multiple zeta values of weight w is generated by th...
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作者：Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras
摘要：In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary (M,g). We show that the boundary distance function, i.e., d(g)vertical bar(x)(partial derivative M)(partial derivative M), known near a point p is an element of partial derivative M at which partial derivative M is strictly convex, determines g in a suitable neighborhood of p in M, up to the natural diffeomorphism invariance of the problem. We also consider the closely related...
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作者：Chang, Huai-Liang; Guo, Shuai; Li, Jun
摘要：We prove two structure theorems for the Gromov-Witten theory of the quintic threefolds, which together give an effective algorithm for the all genus Gromov-Witten potential functions of quintics. By using these structure theorems, we prove Yamaguchi-Yau's Polynomial Ring Conjecture in this paper and prove Bershadsky-Cecotti-Ooguri-Vafa's Feynman rule conjecture in the subsequent paper.
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作者：Cheeger, Jeff; Jiang, Wenshuai; Naber, Aaron
摘要：This paper is concerned with the structure of Gromov-Hausdorff limit d spaces (M-i(n), gi, pi) ->(dGH )(X-n ,d,p) of Riemannian manifolds satisfying a uniform lower Ricci curvature bound RicM(i)(n) >= -(n - 1) as well as the noncollapsing assumption Vol(B-1(p(i))) > v > 0. In such cases, there is a filtration of the singular set, S-0 subset of S-1 center dot center dot center dot Sn-1 := S, where S-k := {x is an element of X : no tangent cone at x is (k +1)-symmetric}. Equivalently, S-k is the...
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作者：Thurston, Dylan P.
摘要：When is a topological branched self-cover of the sphere equivalent to a post-critically finite rational map on CP1? William Thurston gave one answer in 1982, giving a negative criterion (an obstruction to a map being rational). We give a complementary, positive criterion: the branched self-cover is equivalent to a rational map if and only if there is an elastic graph spine for the complement of the post-critical set that gets looser under backwards iteration.
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作者：Smania, Daniel
摘要：We show that in a generic finite-dimensional real-analytic family of real-analytic multimodal maps, the subset of parameters on which the corresponding map has a solenoidal attractor with bounded combinatorics is a set with zero Lebesgue measure.
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作者：Zhou, Xin
摘要：We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms a conjecture by Marques-Neves. We prove that in a bumpy metric each volume spectrum is realized by the min-max value of certain relative homotopy class of sweepouts of boundaries of Caccioppoli sets. The main result follows by approximating such...
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作者：Maderna, Ezequiel; Venturelli, Andrea
摘要：We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h > 0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x, clu) = h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marcha...
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作者：Casale, Guy; Freitag, James; Nagloo, Joel
摘要：We prove the Ax-Lindemann-Weierstrass theorem with derivatives for the uniformizing functions of genus zero Fuchsian groups of the first kind. Our proof relies on differential Galois theory, monodromy of linear differential equations, the study of algebraic and Liouvillian solutions, differential algebraic work of Nishioka towards the Painleve irreducibility of certain Schwarzian equations, and considerable machinery from the model theory of differentially closed fields. Our techniques allow f...
