Project MUSE®: American Journal of Mathematics - Latest Articles
http://muse.jhu.edu/journal/5
Project MUSE®: Latest articles in Africa Today.daily12016-05-05T00:00:00-05:00text/htmlen-USThe Johns Hopkins University PressVol. 118 (1996) through current issueLatest Articles: American Journal of MathematicsTWOProject MUSE®American Journal of Mathematics1080-63770002-9327Latest articles in American Journal of Mathematics. Feed provided by Project MUSE®Cyclic length in the tame Brauer group of the function field of a p-adic curve
http://muse.jhu.edu/article/613783
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Let F be the function field of a smooth curve over the p-adic number field ℚp. We show that for each prime-to-p number n the n-torsion subgroup H2(F,μn)=n Br(F) is generated by ℤ/n-cyclic classes; in fact the ℤ/n-length is equal to two. It follows that the Brauer dimension of F is three (first proved by Saltman), and any F-division algebra of period n and index n2 is
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallCyclic length in the tame Brauer group of the function field of a p-adic curve2016-04-04text/htmlen-USThe Johns Hopkins University PressCyclic length in the tame Brauer group of the function field of a p-adic curve2016-04-042016TWOProject MUSE®243332016-05-05T00:00:00-05:002016-04-04Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature
http://muse.jhu.edu/article/613784
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We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete areaminimizing hypersurfaces exist. Below this value, in contrast, we construct
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallExistence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature2016-04-04text/htmlen-USThe Johns Hopkins University PressExistence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature2016-04-042016TWOProject MUSE®261592016-05-05T00:00:00-05:002016-04-04The Yang-Mills flow and the Atiyah-Bott formula on compact Kähler manifolds
http://muse.jhu.edu/article/613785
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We study the Yang-Mills flow on a holomorphic vector bundle E over a compact Kähler manifold X. Along a solution of the flow, we show that the curvature endomorphism iΛF(At) approaches in L2 an endomorphism with constant eigenvalues given by the slopes of the quotients from the Harder-Narasimhan filtration of E. This proves a sharp lower bound for the Hermitian-Yang-Mills functional and thus the Yang-Mills functional, generalizing to arbitrary dimension a formula of Atiyah and Bott first proven on Riemann surfaces. Furthermore, we show any reflexive extension to all of X of the limiting bundle E∞ is isomorphic to Grhns(E)**, verifying a conjecture of Bando and
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallThe Yang-Mills flow and the Atiyah-Bott formula on compact Kähler manifolds2016-04-04text/htmlen-USThe Johns Hopkins University PressThe Yang-Mills flow and the Atiyah-Bott formula on compact Kähler manifolds2016-04-042016TWOProject MUSE®213552016-05-05T00:00:00-05:002016-04-04Discrete cores of type III free product factors
http://muse.jhu.edu/article/613786
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We give a general description of the discrete decompositions of type III factors arising as central summands of free product von Neumann algebras based on our previous works. This enables us to give several precise structural results on type III free product
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallDiscrete cores of type III free product factors2016-04-04text/htmlen-USThe Johns Hopkins University PressDiscrete cores of type III free product factors2016-04-042016TWOProject MUSE®258022016-05-05T00:00:00-05:002016-04-04Correction to “The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms”
http://muse.jhu.edu/article/613787
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We give a condition under which the findings of the paper by Kenmotsu and Zhou [Amer. J. Math. 122 (2000), no. 2, 295–317] work well and determine the surfaces that were not considered
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallCorrection to “The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms”2016-04-04text/htmlen-USThe Johns Hopkins University PressCorrection to “The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms”2016-04-042016TWOProject MUSE®80812016-05-05T00:00:00-05:002016-04-04Jordan property for Cremona groups
http://muse.jhu.edu/article/613788
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Assuming the Borisov-Alexeev-Borisov conjecture, we prove that there is a constant J = J(n) such that for any rationally connected variety X of dimension n and any finite subgroup G ⊂ Bir(X) there exists a normal abelian subgroup A ⊂ G of index at most J. In particular, we obtain that the Cremona group Cr3 = Bir(ℙ3) enjoys the Jordan
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallJordan property for Cremona groups2016-04-04text/htmlen-USThe Johns Hopkins University PressJordan property for Cremona groups2016-04-042016TWOProject MUSE®278052016-05-05T00:00:00-05:002016-04-04Quantitative level lowering
http://muse.jhu.edu/article/613789
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We give a quantitative version of Ribet’s famous level lowering result for modular forms. Specifically, we measure how certain congruence ideals change as we vary the level. By studying the deformation theory of the Galois representation attached to the modular form, we can use the numerical criterion of Wiles to relate congruence ideals to Selmer groups, and thereby reduce the problem to a calculation in Galois
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallQuantitative level lowering2016-04-04text/htmlen-USThe Johns Hopkins University PressQuantitative level lowering2016-04-042016TWOProject MUSE®226482016-05-05T00:00:00-05:002016-04-04Uniform estimates for Fourier restriction to polynomial curves in ℝd
http://muse.jhu.edu/article/613790
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We prove uniform Lp → Lq bounds for Fourier restriction to polynomial curves in ℝd with affine arclength measure, in the conjectured
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallUniform estimates for Fourier restriction to polynomial curves in ℝd2016-04-04text/htmlen-USThe Johns Hopkins University PressUniform estimates for Fourier restriction to polynomial curves in ℝd2016-04-042016TWOProject MUSE®280702016-05-05T00:00:00-05:002016-04-04Relative shapes of thick subsets of moduli space
http://muse.jhu.edu/article/613791
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A closed hyperbolic surface of genus g ≥ 2 can be decomposed into pairs of pants along shortest closed geodesics and if these curves are sufficiently short (and with lengths uniformly bounded away from 0), then the geometry of the surface is essentially determined by the combinatorics of the pants decomposition. These combinatorics are determined by a trivalent graph, so we call such surfaces trivalent. In this paper, in a first attempt to understand the “shape” of the subset Xg of moduli space consisting of surfaces whose systoles fill, we compare it metrically, asymptotically in g, with the set Yg of trivalent surfaces. As our main result, we find that the set Xg ∩ Yg is metrically “sparse” in Xg (where we equip
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallRelative shapes of thick subsets of moduli space2016-04-04text/htmlen-USThe Johns Hopkins University PressRelative shapes of thick subsets of moduli space2016-04-042016TWOProject MUSE®106632016-05-05T00:00:00-05:002016-04-04Convexity of level sets for elliptic problems in convex domains or convex rings: Two counterexamples
http://muse.jhu.edu/article/613792
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This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings. Constant boundary conditions are imposed on the single component of the boundary when the domain is convex, or on each of the two components of the boundary when the domain is a convex ring. A function is called quasiconcave if its superlevel sets, defined in a suitable way when the domain is a convex ring, are all convex. In this paper, we prove that the superlevel sets of the solutions do not always inherit the convexity or ring-convexity of the domain. Namely, we give two counterexamples to this quasiconcavity property: the first one for some two-dimensional convex
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallConvexity of level sets for elliptic problems in convex domains or convex rings: Two counterexamples2016-04-04text/htmlen-USThe Johns Hopkins University PressConvexity of level sets for elliptic problems in convex domains or convex rings: Two counterexamples2016-04-042016TWOProject MUSE®412242016-05-05T00:00:00-05:002016-04-04Erratum to “The product on smooth and generalized valuations”
http://muse.jhu.edu/article/613793
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Corrections to: S. Alesker and A. Bernig, The product on smooth and generalized valuations, Amer. J. Math. 134 (2012), no. 2
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallErratum to “The product on smooth and generalized valuations”2016-04-04text/htmlen-USThe Johns Hopkins University PressErratum to “The product on smooth and generalized valuations”2016-04-042016TWOProject MUSE®30022016-05-05T00:00:00-05:002016-04-04Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1
http://muse.jhu.edu/article/613794
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In this paper we prove global well-posedness and scattering for the defocusing, one dimensional mass-critical nonlinear Schrödinger equation. We make use of a long-time Strichartz estimate and a frequency localized Morawetz estimate. This continues work begun in earlier papers by the author for dimensions d ≥ 3 and d =
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallGlobal well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 12016-04-04text/htmlen-USThe Johns Hopkins University PressGlobal well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 12016-04-042016TWOProject MUSE®839592016-05-05T00:00:00-05:002016-04-04On uniformly bounded bases in spaces of holomorphic functions
http://muse.jhu.edu/article/613795
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The main result of the paper is the construction of explicit uniformly bounded bases in the spaces of complex homogenous polynomials on the unit ball of C3, extending an earlier result of the author in the C2
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Project MUSE®http://muse.jhu.edu/2016-05-05T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallOn uniformly bounded bases in spaces of holomorphic functions2016-04-04text/htmlen-USThe Johns Hopkins University PressOn uniformly bounded bases in spaces of holomorphic functions2016-04-042016TWOProject MUSE®118052016-05-05T00:00:00-05:002016-04-04