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作者：Riviere, Tristan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces in R-m is given as a nonlinear elliptic equation in divergence form, with non-linearities comprising only Jacobians. Letting (H) over right arrow be the mean curvature vector of the surface, our new formulation reads L (H) over right arrow = 0, where L is a well-defined locally invertible self-adjoint elliptic operator. Several consequences are studied. In particular, the long standing open probl...
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作者：Zhan, Dapeng
作者单位：Yale University
摘要：We derive some geometric properties of chordal SLE(k; (rho) over right arrow) processes. Using these results and the method of coupling two SLE processes, we prove that the outer boundary of the final hull of a chordal SLE(k; (rho) over right arrow) process has the same distribution as the image of a chordal SLE(k'; (rho) over right arrow) trace, where k > 4, k' = 16/k, and the forces (rho) over right arrow and (rho) over right arrow' are suitably chosen. We find that for. = 8, the boundary of...
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作者：Papanikolas, Matthew A.
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.
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作者：Ionescu, A. D.; Kenig, C. E.; Tataru, D.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Chicago; University of California System; University of California Berkeley
摘要：We prove that the KP-I initial-value problem {partial derivative(t)u + partial derivative(3)(x)u - partial derivative(-1)(x)partial derivative(2)(y)u + partial derivative(x)(u(2)/2) = 0 on R-x,y(2) x R-t; u(0) =phi is globally well-posed in the energy space E-1(R-2) = {phi : R-2 -> R : parallel to phi parallel to(E1(R2)) approximate to parallel to phi parallel to(L2) + parallel to partial derivative(x)phi parallel to(L2) + parallel to partial derivative(-1)(x)partial derivative(y)phi parallel ...
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作者：Cluckers, Raf; Loeser, Francois
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); KU Leuven
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作者：Ellenberg, Jordan S.; Venkatesh, Akshay
作者单位：University of Wisconsin System; University of Wisconsin Madison; New York University
摘要：We prove a local-global principle for the problem of representations of quadratic forms by quadratic forms over Z, in codimension >= 5. The proof uses the ergodic theory of p-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.
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作者：Peyre, Emmanuel
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Centre National de la Recherche Scientifique (CNRS)
摘要：Let G be a finite group and W be a faithful representation of G over C. The group G acts on the field of rational functions C(W). The question whether the field of invariant functions C(W)(G) is purely transcendental over C goes back to Emmy Noether. Using the unramified cohomology group of degree 2 of this field as an invariant, Saltman gave the first examples for which C(W)(G) is not rational over C. Around 1986, Bogomolov gave a formula which expresses this cohomology group in terms of the ...
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作者：Li, Simin; Shen, Weixiao
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：In this paper, we study the Hausdorff dimension of Cantor attractors of smooth interval maps with non-flat critical points. We prove that the Hausdorff dimension is bounded from above by a constant less than 1 which depends only on the number and order of the critical points.
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作者：Apostolov, Vestislav; Calderbank, DavidM. J.; Gauduchon, Paul; Tonnesen-Friedman, Christina W.
作者单位：University of Quebec; University of Quebec Montreal; Bulgarian Academy of Sciences; University of Bath; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Union College
摘要：This paper concerns the existence and explicit construction of extremal Kahler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of Hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of the 'admissible' Kahler classes (i.e., those compatible with the ...
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作者：Bray, Hubert; Miao, Pengzi
作者单位：Duke University; Monash University
摘要：Given a surface in an asymptotically flat 3-manifold with nonnegative scalar curvature, we derive an upper bound for the capacity of the surface in terms of the area of the surface and the Willmore functional of the surface. The capacity of a surface is defined to be the energy of the harmonic function which equals 0 on the surface and goes to 1 at infinity. Even in the special case of R-3, this is a new estimate. More generally, equality holds precisely for a spherically symmetric sphere in a...
