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作者：Heckman, Gert; Zhao, Lei
作者单位：Radboud University Nijmegen; Nankai University
摘要：Chenciner and Jim,nez-P,rez (Mosc Math J 13(4):621-630, 2013) showed that the range of the spectra of the angular momenta of all the rigid motions of a fixed central configuration in a general Euclidean space form a convex polytope. In this note we explain how this result follows from a general convexity theorem of O'Shea and Sjamaar in real moment map geometry (Math Ann 31:415-457, 2000). Finally, we provide a representation-theoretic description of the pushforward of the normalized measure u...
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作者：Kollar, Janos; Xu, Chenyang
作者单位：Princeton University
摘要：A log Calabi-Yau pair consists of a proper variety X and a divisor D on it such that is numerically trivial. A folklore conjecture predicts that the dual complex of D is homeomorphic to the quotient of a sphere by a finite group. The main result of the paper shows that the fundamental group of the dual complex of D is a quotient of the fundamental group of the smooth locus of X, hence its pro-finite completion is finite. This leads to a positive answer in dimension 4. We also study the dual co...
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作者：Eckhardt, Jonathan; Kostenko, Aleksey
作者单位：Cardiff University; University of Vienna
摘要：Motivated by the study of certain nonlinear wave equations (in particular, the Camassa-Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form -u = z u omega + z(2) u nu on an interval [0, L), where is a real-valued distribution in H-loc(-1), nu is a non-negative Borel measure on [0, L) and z is a complex spectral parameter. Apart from developing basic spectral theory for these kinds of spectral problems, our main result is ...
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作者：Deraux, Martin; Parker, John R.; Paupert, Julien
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Durham University; Arizona State University; Arizona State University-Tempe
摘要：We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne-Mostow, and fell into nine commensurability classes. Our groups produce five new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete groups acting on the complex hyperbolic plane.
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作者：Gan, Wee Teck; Ichino, Atsushi
作者单位：National University of Singapore; Kyoto University
摘要：We establish the Fourier-Jacobi case of the local Gross-Prasad conjecture for unitary groups, by using local theta correspondence to relate the Fourier-Jacobi case with the Bessel case established by Beuzart-Plessis. To achieve this, we prove two conjectures of Prasad on the precise description of the local theta correspondence for (almost) equal rank unitary dual pairs in terms of the local Langlands correspondence. The proof uses Arthur's multiplicity formula and thus is one of the first exa...
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作者：Filip, Simion
作者单位：University of Chicago
摘要：We prove that invariant subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. This implies that invariant subbundles must vary polynomially on affine manifolds. All results apply to tensor powers of the cocycle and this implies that the measurable and real-analytic algebraic hulls coincide. We also prove that affine manifolds typically parametrize Jacobians with non-trivial endomorphisms. If the...
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作者：Oh, Sung-Jin; Tataru, Daniel
作者单位：University of California System; University of California Berkeley
摘要：This article constitutes the final and main part of a three-paper sequence (Ann PDE, 2016. doi:10.1007/s40818-016-0006-4; Oh and Tataru, 2015. arXiv:1503.01561), whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on R1+4 for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers (Ann PDE, 2016. doi:10.1007/s40818-016-0006-4; Oh and Tataru, 2...
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作者：Inou, Hiroyuki; Mukherjee, Sabyasachi
作者单位：Kyoto University; Constructor University; State University of New York (SUNY) System; Stony Brook University
摘要：It is well known that every rational parameter ray of the Mandelbrot set lands at a single parameter. We study the rational parameter rays of the multicorn , the connectedness locus of unicritical antiholomorphic polynomials of degree d, and give a complete description of their accumulation properties. One of the principal results is that the parameter rays accumulating on the boundaries of odd period (except period 1) hyperbolic components of the multicorns do not land, but accumulate on arcs...
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作者：Berman, Robert J.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the setting of Q-Fano varieties equipped with their anti-canonical polarization. The proof is based on a new formula expressing the Donaldson-Futaki invariants in terms of the slope of the Ding functional along a geodesic ray in the space of all bounded positively curved metrics on the anti-canonical line bundle of X. ...
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作者：Fraser, Ailana; Schoen, Richard
作者单位：University of British Columbia; Stanford University; University of California System; University of California Irvine
摘要：We prove existence and regularity of metrics on a surface with boundary which maximize sigma(1) L where sigma(1) is the first nonzero Steklov eigenvalue and L the boundary length. We show that such metrics arise as the induced metrics on free boundary minimal surfaces in the unit ball B-n for some n. In the case of the annulus we prove that the unique solution to this problem is the induced metric on the critical catenoid, the unique free boundary surface of revolution in B-3. We also show tha...
