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101.
Paolo Lisca 《Proceedings of the American Mathematical Society》2001,129(11):3437-3444
Let be a closed, oriented -manifold. The set of homotopy classes of positive, fillable contact structures on is a subtle invariant of , known to always be a finite set. In this paper we study under the assumption that carries metrics with positive scalar curvature. Using Seiberg-Witten gauge theory, we prove that two positive, fillable contact structures on are homotopic if and only if they are homotopic on the complement of a point. This implies that the cardinality of is bounded above by the order of the torsion subgroup of . Using explicit examples we show that without the geometric assumption on such a bound can be arbitrarily far from holding.
102.
Shiffman proved his famous first theorem, that if A R3 is a compact minimal annulus bounded by two convex Jordan curves in parallel (say horizontal) planes, then A is foliated by strictly convex horizontal Jordan curves. In this article we use Perron's method to construct minimal annuli which have a planar end and are bounded by two convex Jordan curves in horizontal planes, but the horizontal level sets of the surfaces are not all convex Jordan curves or straight lines. These surfaces show that unlike his second and third theorems, Shiffman's first theorem is not generalizable without further qualification. 相似文献
103.
FANG FUQUAN 《数学年刊B辑(英文版)》2000,(4)
1. IntroductionBy [111, a hypersurface in a symmetric space is called equifocal if every normal geodesicperpendiculajr to it is closed of constant length, say l, and contains Zg focal points for somepositive integer g. This is a natural generalization of isoparametric hypersurfaces in sphereswhere the illteger g is the number of distinct principal curvatures. In this note we considerequifocal hypersurfaces in simply connected rank one symmetric spaces, i.e. the complexprojective space CP", th… 相似文献
104.
Large volume growth and finite topological type 总被引:5,自引:0,他引:5
D. Ordway B. Stephens D. G. Yang 《Proceedings of the American Mathematical Society》2000,128(4):1191-1196
It is shown in this paper that a complete noncompact -dimensional Riemannian manifold with nonnegative Ricci curvature, sectional curvature bounded from below, and large volume growth is of finite topological type provided that the volume growth rate of the complement of the cone of rays from a fixed base point is less than .
105.
Matthieu Fradelizi 《Proceedings of the American Mathematical Society》2000,128(9):2735-2744
We define the sectional bodies associated to a convex body in and two related measures of symmetry. These definitions extend those of Grünbaum (1963). As Grünbaum conjectured, we prove that the simplices are the most dissymmetrical convex bodies with respect to these measures. In the case when the convex body has a sufficiently smooth boundary, we investigate some limit behaviours of the volume of the sectional bodies.
106.
We investigated the propagation and transformation of laser beams and the formation of caustics in particular directions,
including optical axes of crystals. We found a direct connection between the particular directions and the curvature of wave
surfaces that is determined by the symmetry and optical properties of the crystals. We demonstrated that caustics in particular
directions are characterized by a degree of the curvature degeneracy and are described by particular solutions of the corresponding
nonlinear equations.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 4, pp. 491–498, July–August, 2007. 相似文献
107.
In this report, we demonstrate the efficient generation of collinearly propagating photon pairs in a bulk periodically poled potassium titanyl phosphate pumped by a cw laser. The detected coincidence counts are more than 7400/s with 3.58 mW pump power in a Hanbury-Brown-Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/mW. This is very promising for some applications, such as quantum key distribution, proof of the Bell-inequality, preparation of single photon states in broadband wave packets, Franson-type interference and so on. 相似文献
108.
ZHAO Meishan 《理论物理通讯》1999,31(1):21-26
We present a dilatation transformation anlysis on curvilinear reaction path, andanalyze the curvature effect of complex scaling on the prediction of molecular reaction thresholdresonance. An example of numerical calculation was carried out for the prediction of thresholdresonance of H + H2 molecular scattering with and without consideration of the reactionpath curvature. We found, in the studied system, that the curvature provides a correction tothreshold resonance lifetime as large as 25%. 相似文献
109.
A logarithmic Gauss curvature flow and the Minkowski problem 总被引:1,自引:0,他引:1
Kai-Seng Chou Xu-Jia Wang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2000,17(6):733
Let X0 be a smooth uniformly convex hypersurface and f a postive smooth function in Sn. We study the motion of convex hypersurfaces X(·,t) with initial X(·,0)=θX0 along its inner normal at a rate equal to log(K/f) where K is the Gauss curvature of X(·,t). We show that the hypersurfaces remain smooth and uniformly convex, and there exists θ*>0 such that if θ<θ*, they shrink to a point in finite time and, if θ>θ*, they expand to an asymptotic sphere. Finally, when θ=θ*, they converge to a convex hypersurface of which Gauss curvature is given explicitly by a function depending on f(x). 相似文献
110.
Sharief Deshmukh 《Annali di Matematica Pura ed Applicata》2008,187(1):59-65
In this paper we study the role of constant vector fields on a Euclidean space R
n+p
in shaping the geometry of its compact submanifolds. For an n-dimensional compact submanifold M of the Euclidean space R
n+p
with mean curvature vector field H and a constant vector field on R
n+p
, the smooth function is used to obtain a characterization of sphere among compact submanifolds of positive Ricci curvature (cf. main Theorem).
相似文献