Project MUSE®: American Journal of Mathematics - Latest Articles
http://muse.jhu.edu/journal/5
Project MUSE®: Latest articles in American Journal of Mathematics.daily12017-04-30T00:00:00-05:00text/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®Topological tameness of Margulis Spacetimes
http://muse.jhu.edu/article/652516
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We show that Margulis spacetimes without parabolic holonomy elements are topologically tame. A Margulis spacetime is the quotient of the 3-dimensional Minkowski space by a free proper isometric action of the free group of rank ≥ 2. We will use our particular point of view that the Margulis spacetime is a manifold-with-boundary with an ℝP3-structure in an essential way. The basic tools are a bordification by a closed ℝP2-surface with free holonomy group, and the work of Goldman, Labourie, and Margulis on geodesics in the Margulis spacetimes and 3-manifold
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallTopological tameness of Margulis Spacetimes2017-03-30text/htmlen-USThe Johns Hopkins University PressTopological tameness of Margulis Spacetimes2017-03-302017TWOProject MUSE®494952017-04-30T00:00:00-05:002017-03-30Double Pieri algebras and iterated Pieri algebras for the classical groups
http://muse.jhu.edu/article/652517
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We study iterated Pieri rules for representations of classical groups. That is, we consider tensor products of a general representation with multiple factors of representations corresponding to one-rowed Young diagrams (or in the case of the general linear group, also the duals of these). We define iterated Pieri algebras, whose structure encodes the irreducible decompositions of such tensor products. We show that there is a single family of algebras, which we call double Pieri algebras, and which can be used to describe the iterated Pieri algebras for all three families of classical groups. Furthermore, we show that the double Pieri algebras have flat deformations to Hibi rings on explicitly described posets. As
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallDouble Pieri algebras and iterated Pieri algebras for the classical groups2017-03-30text/htmlen-USThe Johns Hopkins University PressDouble Pieri algebras and iterated Pieri algebras for the classical groups2017-03-302017TWOProject MUSE®580762017-04-30T00:00:00-05:002017-03-30Liouville and Calabi-Yau type theorems for complex Hessian equations
http://muse.jhu.edu/article/652518
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We prove a Liouville type theorem for entire maximal m-subharmonic functions in ℂn with bounded gradient. This result, coupled with a standard blow-up argument, yields a (nonexplicit) a priori gradient estimate for the complex Hessian equation on a compact Kähler manifold. This terminates the program, initiated by Hou, Ma, and Wu, of solving the non-degenerate Hessian equation on such manifolds in full generality. We also obtain, using our previous work, continuous weak solutions in the degenerate case for the right-hand side in some Lp, with a sharp bound on
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallLiouville and Calabi-Yau type theorems for complex Hessian equations2017-03-30text/htmlen-USThe Johns Hopkins University PressLiouville and Calabi-Yau type theorems for complex Hessian equations2017-03-302017TWOProject MUSE®195772017-04-30T00:00:00-05:002017-03-30Insufficiency of the étale Brauer-Manin obstruction: Towards a simply connected example
http://muse.jhu.edu/article/652519
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Since Poonen’s construction of a variety X defined over a number field k for which X(k) is empty and the étale Brauer-Manin set X(Ak)Br,ét is not, several other examples of smooth, projective varieties have been found for which the étale Brauer-Manin obstruction does not explain the failure of the Hasse principle. All known examples are constructed using “Poonen’s trick”, i.e., they have the distinctive feature of being fibrations over a higher genus curve; in particular, their Albanese variety is non-trivial. In this paper, we construct examples for which the Albanese variety is trivial. The new geometric ingredient in our construction is the appearance of Beauville surfaces. Assuming the abc conjecture and using
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallInsufficiency of the étale Brauer-Manin obstruction: Towards a simply connected example2017-03-30text/htmlen-USThe Johns Hopkins University PressInsufficiency of the étale Brauer-Manin obstruction: Towards a simply connected example2017-03-302017TWOProject MUSE®147582017-04-30T00:00:00-05:002017-03-30On finite Morse index solutions of higher order fractional Lane-Emden equations
http://muse.jhu.edu/article/652520
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We classify finite Morse index solutions of the following nonlocal Lane-Emden equation (–∆)s u = |u|p–1u ℝn for 1 < s < 2 via a novel monotonicity formula. For local cases s = 1 and s = 2 this classification was provided by Farina in 2007 and Dávila, Dupaigne, Wang, and Wei in 2014, respectively. Moreover, for the nonlocal case 0 < s <1 finite Morse index solutions are classified by Dávila, Dupaigne, and Wei in their 2014
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallOn finite Morse index solutions of higher order fractional Lane-Emden equations2017-03-30text/htmlen-USThe Johns Hopkins University PressOn finite Morse index solutions of higher order fractional Lane-Emden equations2017-03-302017TWOProject MUSE®199302017-04-30T00:00:00-05:002017-03-30Entirety of cuspidal Eisenstein series on loop groups
http://muse.jhu.edu/article/652521
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In this paper, we prove the entirety of loop group Eisenstein series induced from cusp forms on the underlying finite dimensional group, by demonstrating their absolute convergence on the full complex plane. This is quite in contrast to the finite-dimensional setting, where such series only converge absolutely in a right half plane (and have poles elsewhere coming from L-functions in their constant terms). Our result is the ℚ-analog of a theorem of A. Braverman and D. Kazhdan from the function field setting, who previously showed the analogous Eisenstein series there are finite
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallEntirety of cuspidal Eisenstein series on loop groups2017-03-30text/htmlen-USThe Johns Hopkins University PressEntirety of cuspidal Eisenstein series on loop groups2017-03-302017TWOProject MUSE®322652017-04-30T00:00:00-05:002017-03-30Finiteness of 2-reflective lattices of signature (2,n)
http://muse.jhu.edu/article/652522
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A modular form for an even lattice L of signature (2,n) is said to be 2-reflective if its zero divisor is set-theoretically contained in the Heegner divisor defined by the (−2)-vectors in L. We prove that there are only finitely many even lattices with n ≥ 7 which admit 2-reflective modular forms. In particular, there is no such lattice in n ≥ 26 except the even unimodular lattice of signature (2,26). This proves a conjecture of Gritsenko and Nikulin in the range n ≥
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallFiniteness of 2-reflective lattices of signature (2,n)2017-03-30text/htmlen-USThe Johns Hopkins University PressFiniteness of 2-reflective lattices of signature (2,n)2017-03-302017TWOProject MUSE®170472017-04-30T00:00:00-05:002017-03-30Extremal functions in de Branges and Euclidean spaces, II
http://muse.jhu.edu/article/652523
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This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of Beurling and Selberg and provide a variety of applications in analysis and analytic number theory. Here we majorize and minorize (on ℝN) the Gaussian x ↦ e−πλ|x|2, where λ > 0 is a free parameter, by functions with distributional Fourier transforms supported on Euclidean balls, optimizing weighted L1-errors. By integrating the parameter λ against suitable measures, we solve the analogous problem for a wide class of radial functions. Applications to inequalities and periodic
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Project MUSE®http://muse.jhu.edu/2017-04-30T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallExtremal functions in de Branges and Euclidean spaces, II2017-03-30text/htmlen-USThe Johns Hopkins University PressExtremal functions in de Branges and Euclidean spaces, II2017-03-302017TWOProject MUSE®379632017-04-30T00:00:00-05:002017-03-30