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作者：Enciso, Alberto; Peralta-Salas, Daniel
摘要：Given any possibly unbounded, locally finite link, we show that there exists a smooth diffeomorphism transforming this link into a set of stream (or vortex) lines of a vector field that solves the steady incompressible Euler equation in R-3. Furthermore, the diffeomorphism can be chosen arbitrarily close to the identity in any C-r norm.
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作者：Castro, Angel; Cordoba, Diego; Fefferman, Charles; Gancedo, Francisco; Lopez-Fernandez, Maria
摘要：The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.
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作者：Caro, Daniel; Tsuzuki, Nobuo
摘要：We prove the overholonomicity of overconvergent F-isocrystals over smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent F-isocrystals are equivalent. Then the overholonomicity is stable under tensor products. So, the overholonomicity gives a p-adic cohomology stable under Grothendieck's cohomological operations.
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作者：Mineyev, Igor
摘要：In this article, we define submultiplicativity of l(2)-numbers in the category of F-complexes over a given F-complex X, which generalizes the statement of the Strengthened Hanna Neumann Conjecture (SHNC). In the case when F is a left-orderable group and X is a free F-complex, we prove submultiplicativity for the subcategory consisting of F-ordered leafages over X with an additional analytic assumption called the deep-fall property. We show that the deep-fall property is satisfied for graphs. T...
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作者：Feher, L. M.; Rimanyi, R.
摘要：Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic combinatorics. The main obstacle of their widespread application is that only a few, sporadic Thom polynomials have been known explicitly. In this paper we develop a general method for calculating Thom polynomials of contact singularities. Along t...
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作者：Calaque, Damien; Rossi, Carlo A.; Van den Bergh, Michel
摘要：In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over polyvector fields and on Hochschild homology over Hochschild cohomology. In fact we show that twisting with the square root of the Todd class gives an isomorphism of precalculi between these pairs of objects. Our methods use formal geometry to globalize the local formality quasi-isomorphisms introduced by Kontsevich and Shoikhet. (The existence of the latt...
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作者：Helton, J. William; McCullough, Scott
摘要：The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex free basic open semi-algebraic set. The main theorem of this paper is a converse, each such set arises from some LMI. The result has implications for semi-definite programming and systems engineering as well as for free semi-algebraic geometry.
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作者：de Cataldo, Mark Andrea A.; Hausel, Tamas; Migliorini, Luca
摘要：For G = GL(2), PGL(2), SL2 we prove that the perverse filtration associated with the Hitchin map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a compact Riemann surface C agrees with the weight filtration on the rational cohomology of the twisted G character variety of C when the cohomologies are identified via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.
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作者：Parnovski, Leonid; Shterenberg, Roman
摘要：We prove the complete asymptotic expansion of the integrated density of states of a Schrodinger operator H = -Delta + b acting in R-d when the potential b is either smooth periodic, or generic quasi-periodic (finite linear combination of exponentials), or belongs to a wide class of almost-periodic functions.
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作者：Ivarsson, Bjoern; Kutzschebauch, Frank
摘要：We solve Gromov's Vaserstein problem. Namely, we show that a null-homotopic holomorphic mapping from a finite dimensional reduced Stein space into SLn (C) can be factored into a finite product of unipotent matrices with holomorphic entries.
