Project MUSE®: American Journal of Mathematics - Latest Articles
http://muse.jhu.edu/journal/5
Project MUSE®: Latest articles in American Journal of Mathematics.daily12017-01-22T00:00:00-05:00text/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®On the Muskat problem: Global in time results in 2D and 3D
http://muse.jhu.edu/article/640893
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This paper considers the three-dimensional Muskat problem in the stable regime.We obtain a conservation law which provides an L2 maximum principle for the fluid interface. We also show global in time existence for strong and weak solutions with initial data controlled by explicit constants. Furthermore we refine the available estimates to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2D. Finally we provide global in time results in spaces with critical regularity, giving solutions with bounded slope and time integrable bounded
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallOn the Muskat problem: Global in time results in 2D and 3D2016-12-09text/htmlen-USThe Johns Hopkins University PressOn the Muskat problem: Global in time results in 2D and 3DViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®178952017-01-22T00:00:00-05:002016-12-09Discrete maximal functions in higher dimensions and applications to ergodic theory
http://muse.jhu.edu/article/640894
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We establish a higher dimensional counterpart of Bourgain’s pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates Vr on Lp spaces for all 1 < p ∞ and r > max{p,p/(p − 1)}. Moreover, we obtain the estimates which are uniform in the coefficients of a polynomial mapping of fixed
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallDiscrete maximal functions in higher dimensions and applications to ergodic theory2016-12-09text/htmlen-USThe Johns Hopkins University PressDiscrete maximal functions in higher dimensions and applications to ergodic theoryViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®341292017-01-22T00:00:00-05:002016-12-09Covers of tori over local and global fields
http://muse.jhu.edu/article/640895
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Langlands has described the irreducible admissible representations of T, when T is the group of points of an algebraic torus over a local field. Also, Langlands described the automorphic representations of when is the group of adelic points of an algebraic torus over a global field F. We describe irreducible (in the local setting) and automorphic (in the global setting) ∊-genuine representations for “covers” of tori, also known as “metaplectic tori,” which arise from a framework of Brylinski and Deligne. In particular, our results include a description of spherical Hecke algebras in the local unramified setting, and a global multiplicity estimate for automorphic representations of covers of split tori. For
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallCovers of tori over local and global fields2016-12-09text/htmlen-USThe Johns Hopkins University PressCovers of tori over local and global fieldsViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®198972017-01-22T00:00:00-05:002016-12-09Moments and valuations
http://muse.jhu.edu/article/640896
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All measurable and SL(n)-covariant vector valued valuations on convex polytopes containing the origin in their interiors are completely classified. The moment vector is shown to be essentially the only such
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallMoments and valuations2016-12-09text/htmlen-USThe Johns Hopkins University PressMoments and valuationsViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®364552017-01-22T00:00:00-05:002016-12-09Nodal intersections for random eigenfunctions on the torus
http://muse.jhu.edu/article/640897
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We investigate the number of nodal intersections of random Gaussian Laplace eigenfunctions on the standard two-dimensional flat torus (“arithmetic random waves”) with a fixed smooth reference curve with nonvanishing curvature. The expected intersection number is universally proportional to the length of the reference curve, times the wavenumber, independent of the geometry. Our main result prescribes the asymptotic behavior of the nodal intersections variance for smooth curves in the high energy limit; remarkably, it is dependent on both the angular distribution of lattice points lying on the circle with radius corresponding to the given wavenumber, and the geometry of the given curve. In particular, this implies
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallNodal intersections for random eigenfunctions on the torus2016-12-09text/htmlen-USThe Johns Hopkins University PressNodal intersections for random eigenfunctions on the torusViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®238742017-01-22T00:00:00-05:002016-12-09The essential skeleton of a degeneration of algebraic varieties
http://muse.jhu.edu/article/640898
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In this paper, we explore the connections between the Minimal Model Program and the theory of Berkovich spaces. Let k be a field of characteristic zero and let X be a smooth and projective k((t))-variety with semi-ample canonical divisor. We prove that the essential skeleton of X coincides with the skeleton of any minimal dlt-model and that it is a strong deformation retract of the Berkovich analytification of X. As an application, we show that the essential skeleton of a Calabi-Yau variety over k((t)) is a
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallThe essential skeleton of a degeneration of algebraic varieties2016-12-09text/htmlen-USThe Johns Hopkins University PressThe essential skeleton of a degeneration of algebraic varietiesViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®221572017-01-22T00:00:00-05:002016-12-09Quadratic base change and the analytic continuation of the Asai L-function: A new trace formula approach
http://muse.jhu.edu/article/640899
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Using Langlands’s beyond endoscopy idea, we study the Asai L-function associated to a real quadratic field /ℚ. We prove that the Asai L-function associated to a cuspidal automorphic representation over has analytic continuation to the complex plane with at most a simple pole at s = 1. We then show if the L-function has a pole then the representation is a base change from ℚ. While this result is known using integral representations from the work of Asai and Flicker, the approach here uses novel analytic number techniques and gives a deeper understanding of the geometric side of the relative trace formula. Moreover, the approach in this paper will make it easier to grasp more complicated functoriality via beyond
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallQuadratic base change and the analytic continuation of the Asai L-function: A new trace formula approach2016-12-09text/htmlen-USThe Johns Hopkins University PressQuadratic base change and the analytic continuation of the Asai L-function: A new trace formula approachViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®250932017-01-22T00:00:00-05:002016-12-09Canonical bases in tensor products revisited
http://muse.jhu.edu/article/640900
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We construct canonical bases in tensor products of several lowest and highest weight integrable modules, generalizing Lusztig’s
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallCanonical bases in tensor products revisited2016-12-09text/htmlen-USThe Johns Hopkins University PressCanonical bases in tensor products revisitedViscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®104172017-01-22T00:00:00-05:002016-12-09Index to Volume 138, 2016
http://muse.jhu.edu/article/640901
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Project MUSE®http://muse.jhu.edu/2017-01-22T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallIndex to Volume 138, 20162016-12-09text/htmlen-USThe Johns Hopkins University PressIndex to Volume 138, 2016Viscous flowFluid dynamicsSurfaces, AlgebraicAmerican journal of mathematics2016-12-092016TWOProject MUSE®147352017-01-22T00:00:00-05:002016-12-09