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作者:Ioan Bejenaru
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.307, pp.1151-1183Elsevier
摘要:Abstract(#br)In [4] nearly optimal L 1 trilinear restriction estimates in R n + 1 are established under transversality assumptions only. In this paper we show that the curvature improves the range of exponents, by establishing L p estimates, for any p > 2 ( n + 4 ) 3 ( n + 2 ) in...
作者:Dylan G.L. Allegretti , Hyun Kyu Kim
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.306, pp.1164-1208Elsevier
摘要:Abstract(#br)We define a canonical map from a certain space of laminations on a punctured surface into the quantized algebra of functions on a cluster variety. We show that this map satisfies a number of special properties conjectured by Fock and Goncharov. Our construction ...
作者:Ai-Jun Li , Dongmeng Xi , Gaoyong Zhang
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.304, pp.494-538Elsevier
摘要:Abstract(#br)The L p cosine transform on Grassmann manifolds naturally induces finite dimensional Banach norms whose unit balls are origin-symmetric convex bodies in R n . Reverse isoperimetric type volume inequalities for these bodies are established, which extend results from t...
作者:Roi Docampo , Antonio Nigro
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.306, pp.1269-1332Elsevier
摘要:Abstract(#br)We study the arc space of the Grassmannian from the point of view of the singularities of Schubert varieties. Our main tool is a decomposition of the arc space of the Grassmannian that resembles the Schubert cell decomposition of the Grassmannian itself. Just as the ...
作者:Victoria Lebed , Leandro Vendramin
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.304, pp.1219-1261Elsevier
摘要:Abstract(#br)This paper deals with left non-degenerate set-theoretic solutions to the Yang–Baxter equation (= LND solutions), a vast class of algebraic structures encompassing groups, racks, and cycle sets. To each such solution there is associated a shelf (i.e., a self-dist...
作者:M.L. Lapidus , G. Radunović , D. Žubrinić
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.307, pp.1215-1267Elsevier
摘要:Abstract(#br)Recently, the first author has extended the definition of the zeta function associated with fractal strings to arbitrary bounded subsets A of the N -dimensional Euclidean space R N , for any integer N ≥ 1 . It is defined by the Lebesgue integral ζ A ( s ) =...
作者:Lorenzo Brasco , Erik Lindgren
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.304, pp.300-354Elsevier
摘要:Abstract(#br)We prove that for p ≥ 2 , solutions of equations modeled by the fractional p -Laplacian improve their regularity on the scale of fractional Sobolev spaces. Moreover, under certain precise conditions, they are in W loc 1 , p and their gradients are in a fractiona...
作者:Sergey Grigorian
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.308, pp.142-207Elsevier
摘要:Abstract(#br)We use a G 2 -structure on a 7-dimensional Riemannian manifold with a fixed metric to define an octonion bundle with a fiberwise non-associative product. We then define a metric-compatible octonionic covariant derivative on this bundle that is compatible with the oct...
作者:Aaron Bertram , Robert Easton
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.308, pp.36-82Elsevier
摘要:Abstract(#br)We develop the foundations of a theory of algebraic geometry for semirings, concentrating mainly on the semiring of tropical polynomials. Replacing ideals with the more general notion of congruences, we establish a relationship between congruences on the semiring of ...
作者:Thierry De Pauw , Antoine Lemenant , Vincent Millot
来源:[J].Advances in Mathematics(IF 1.373), 2017, Vol.305, pp.1268-1319Elsevier
摘要:Abstract(#br)We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show C 1 regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condit...

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