共查询到20条相似文献,搜索用时 234 毫秒
1.
In this paper, we will introduce the notion of harmonic stability for complete minimal hypersurfaces in a complete Riemannian
manifold. The first result we prove, is that a complete harmonic stable minimal surface in a Riemannian manifold with non-negative
Ricci curvature is conformally equivalent to either a plane R
2 or a cylinder R × S
1, which generalizes a theorem due to Fischer-Colbrie and Schoen [12].
The second one is that an n ≥ 2-dimensional, complete harmonic stable minimal, hypersurface M in a complete Riemannian manifold with non-negative sectional curvature has only one end if M is non-parabolic. The third one, which we prove, is that there exist no non-trivial L
2-harmonic one forms on a complete harmonic stable minimal hypersurface in a complete Riemannian manifold with non-negative
sectional curvature. Since the harmonic stability is weaker than stability, we obtain a generalization of a theorem due to
Miyaoka [20] and Palmer [21].
Research partially Supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science
and Technology, Japan.
The author’s research was supported by grant Proj. No. KRF-2007-313-C00058 from Korea Research Foundation, Korea.
Authors’ addresses: Qing-Ming Cheng, Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga
840-8502, Japan; Young Jin Suh, Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea 相似文献
2.
This paper examines the role communication between players might serve in enabling them to reach an agreement on the future
play of a repeated game. The property of the communication process that we focus on is the amount of time it takes to complete.
We characterize the effects of such communication processes indirectly by determining the set of agreements they may yield.
A weak and a strong criterion are introduced to describe sets of agreements that are “stable” in the sense that players would
follow the current agreement and not seek to reach a new agreement. We show that as players become extremely patient, strongly
stable sets converge to Pareto efficient singletons. We apply the stability criteria to Prisoner’s Dilemmas and show how the
unique strongly stable set reflects asymmetries in the players’ stage-game payoffs. Finally, we model the communication process
as a Rubinstein alternating-offer bargaining game and demonstrate that the resulting agreements help characterize the strongly
stable set for a general class of communication mechanisms.
Received January 1998/final version June 1999 相似文献
3.
In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled
by a modified Darcy’s law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The
purpose of this paper is to identify the steady states of this flow and to study their stability.
The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the
bottom is constant then the corresponding steady state is asymptotically stable.
相似文献
4.
We prove a complete converse of Aliprantis and Burkinshaw’s Theorem [2]. Also we obtain a generalization of Wickstead’s Theorem
[9] about this converse, and we give some interesting consequences.
revised 4 April, 18 October, and 26 December 2005 相似文献
5.
Malay Ghosh 《Annals of the Institute of Statistical Mathematics》1975,27(1):57-68
Summary The object of the present investigation is to study some properties of a class of Spearman rank statistics and to apply these
results in studying the properties of a sequential procedure proposed in Section 3. The problem is one of bounded length confidence
intervals for simple regression coefficients in linear models where both variables are subject to error. It is shown that
the proposed procedure is asymptotically ‘consistent’ and ‘efficient’ in the sense of Chow and Robbins [3]. 相似文献
6.
Rong-Qing Jia Ka-Sing Lau Ding-Xuan Zhou 《Journal of Fourier Analysis and Applications》2001,7(2):143-167
In the recent characterizations of the Lp solution of the refinement equation in terms of the “p-norm joint spectral radius,” there are problems in choosing the initial
function for iteration [3, 23], or in addition, requiring stability of the refinable function [13, 17]. In this article we
overcome these difficulties and give a more complete characterization of this nature. The criterion is constructive and can
be implemented. It can be used to describe the regularity of the solution without assuming stability. This has significant
advantages over the previous work. The corresponding results for vector refinement equations are also discussed. 相似文献
7.
We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton [BF99 ]. All four formulae are combinatorial, in the sense that they are expressed
in terms of combinatorial objects of certain types: Zelevinsky permutations, lacing diagrams, Young tableaux, and pipe dreams
(also known as rc-graphs). Three of our formulae are multiplicity-free and geometric, meaning that their summands have coefficient
1 and correspond bijectively to components of a torus-invariant scheme. The remaining (presently non-geometric) formula is
a variant of the conjecture of Buch and Fulton in terms of factor sequences of Young tableaux [BF99 ]; our proof of it proceeds
by way of a new characterization of the tableaux counted by quiver constants. All four formulae come naturally in “doubled”
versions, two for double quiver polynomials, and the other two for their stable limits, the double quiver functions, where setting half the variables equal to the other
half specializes to the ordinary case.
Our method begins by identifying quiver polynomials as multidegrees [BB82 , Jos84 , BB85 , Ros89 ] via equivariant Chow groups
[EG98 ]. Then we make use of Zelevinsky’s map from quiver loci to open subvarieties of Schubert varieties in partial flag
manifolds [Zel85 ]. Interpreted in equivariant cohomology, this lets us write double quiver polynomials as ratios of double
Schubert polynomials [LS82 ] associated to Zelevinsky permutations; this is our first formula. In the process, we provide
a simple argument that Zelevinsky maps are scheme-theoretic isomorphisms (originally proved in [LM98 ]). Writing double Schubert
polynomials in terms of pipe dreams [FK96 ] then provides another geometric formula for double quiver polynomials, via [KM05
]. The combinatorics of pipe dreams for Zelevinsky permutations implies an expression for limits of double quiver polynomials
in terms of products of Stanley symmetric functions [Sta84 ]. A degeneration of quiver loci (orbit closures of GL on quiver representations) to unions of products of matrix Schubert varieties [Ful92 , KM05 ] identifies the summands in
our Stanley function formula combinatorially, as lacing diagrams that we construct based on the strands of Abeasis and Del
Fra in the representation theory of quivers [AD80 ]. Finally, we apply the combinatorial theory of key polynomials to pass
from our lacing diagram formula to a double Schur function formula in terms of peelable tableaux [RS95a , RS98 ], and from
there to our formula of Buch–Fulton type. 相似文献
8.
We present a generalization for the procedure of taking Bruck-Reilly extensions, and we characterize abstractly the regular
semigroups which can be obtained in this way. We shall in particular characterize the regular semigroups which can be obtained
by considering the usual Bruck-Reilly extensions. Our procedure generalizes Munn’s construction [3] which in its turn combines
ideas used by Bruck [1] and Reilly [4]. 相似文献
9.
Mario Krnić Josip Pečarić Predrag Vuković 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):349-357
In this paper we obtain an extension of discrete Hilbert’s inequality, by using some numerical methods. We shall obtain, in
a similar way as Yang did in [10], that the parameter from the kernel can be taken from the interval [3/2, 3). We also compare
our findings with existing results, known from the literature. 相似文献
10.
We add two sections to [8] and answer some questions asked there. In the first section we give another derivation of Theorem
1.1 of [8], which reveals the relation between the entropy formula, (1.4) of [8], and the well-known Li-Yau ’s gradient estimate.
As a by-product we obtain the sharp estimates on ‘Nash’s entropy’ for manifolds with nonnegative Ricci curvature. We also
show that the equality holds in Li-Yau’s gradient estimate, for some positive solution to the heat equation, at some positive
time, implies that the complete Riemannian manifold with nonnegative Ricci curvature is isometric to ℝ
n
.In the second section we derive a dual entropy formula which, to some degree, connects Hamilton’s entropy with Perelman ’s
entropy in the case of Riemann surfaces. 相似文献
11.
Francesco Baldassarri 《Milan Journal of Mathematics》2005,73(1):237-258
We review the notion of regular singular point of a linear differential equation with meromorphic coefficients, from the viewpoint
of algebraic geometry. We give several equivalent definitions of regularity along a divisor for a meromorphic connection on
a complex algebraic manifold and discuss the global birational theory of fuchsian differential modules over a field of algebraic
functions. We describe the generalized algebraic version of Deligne’s canonical extension, constructed in [1, I.4].
Our main interest lies in the algebraic form of Deligne’s regularity criterion [2, II.4.4 (iii)], asserting that, on a normal
compactification, only one codimensional components of the locus at infinity need to be considered. If one considers the purely
algebraic nature of the statement, it is surprising that the only existing proof of this criterion is the transcendental argument
given by Deligne in his corrigendum to loc. cit. dated April 1971. The algebraic proof given in our book [1, I.5.4] is also incorrect, as J. Bernstein kindly indicated to
us.We introduce some notions of logarithmic geometry to let the reader appreciate Bernstein’s (counter)examples to some statements
in our book [1]. Standard methods of generic projection in projective spaces reduce the question to a two-dimensional puzzle.
We report on ongoing correspondence with Y. André and N. Tsuzuki, leading to partial results and provide examples indicating
the subtlety of the problem.
Lecture held in the Seminario Matematico e Fisico on January 31, 2005 Received: June 2005 相似文献
12.
Noritsugu Nakanishi 《International Journal of Game Theory》2009,38(2):249-261
We examine an n-player prisoners’ dilemma game in which only individual deviations are allowed, while coalitional deviations (even non-binding
ones) are not, and every player is assumed to be sufficiently farsighted to understand not only the direct outcome of his
own deviation but also the ultimate outcome resulting from a chain of subsequent deviations by other players. We show that
there exists a unique, noncooperative farsighted stable set (NFSS) and that it supports at least one (partially and/or fully)
cooperative outcome, which is individually rational and Pareto-efficient. We provide a sufficient condition for full cooperation.
Further, we discuss the relationship between NFSS and other “stable set” concepts such as the (myopic) von Neumann–Morgenstern
stable set, Harsanyi (1974)’s strictly stable set, Chwe (1994)’s largest consistent set, and the cooperative farsighted stable
set examined by Suzuki and Muto (2005).
The author is very grateful to Professor Eiichi Miyagawa, the editor and the associate editor of this journal for their insightful
comments and suggestions. He also acknowledges the financial support of Japan Society for the Promotion of Science [Grant-in-Aid
for Scientific Research (C), No. 18530175]. 相似文献
13.
Jens Hornbostel 《manuscripta mathematica》2008,125(3):273-284
We show that the oriented Chow groups of Barge–Morel appear in the E
2-term of the coniveau spectral sequence for Hermitian K-theory. This includes a localization theorem and the Gersten conjecture (over infinite base fields) for Hermitian K-theory. We also discuss the conjectural relationship between oriented and higher oriented Chow groups and Levine’s homotopy
coniveau spectral sequence when applied to Hermitian K-theory. 相似文献
14.
Paolo Aluffi 《Selecta Mathematica, New Series》2005,11(2):155-202
We introduce a notion of integration on the category of proper birational maps to a given variety X, with value in an associated Chow group. Applications include new birational invariants; comparison results for Chern classes
and numbers of nonsingular birational varieties; ‘stringy’ Chern classes of singular varieties; and a zeta function specializing
to the topological zeta function.
In its simplest manifestation, the integral gives a new expression for Chern–Schwartz–MacPherson classes of possibly singular
varieties, placing them into a context in which a ‘change-of-variable’ formula holds. 相似文献
15.
Abstract We prove in details the higher codimensional version of Theorem 1.1 [11]. This provides a complete proof of Fefferman’s SAK
Principle for a class of PDO’s with symplectic characteristic manifold.
Keywords: A priori estimates, General theory of PDO’s 相似文献
16.
In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular,
we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and
contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal
to 2n − 2, is exactly 2n − 2 if and only if the cone is a bipyramidal cone, where n > 1 is the dimension of the cone. Finally, we characterize all toric varieties whose associated cones are complete intersection
cones.
Received: 4 July 2005 相似文献
17.
Jonathan Kirby 《Selecta Mathematica, New Series》2009,15(3):445-486
The complete first-order theories of the exponential differential equations of semiabelian varieties are given. It is shown
that these theories also arise from an amalgamation-with-predimension construction in the style of Hrushovski. The theories
include necessary and sufficient conditions for a system of equations to have a solution. The necessary conditions generalize
Ax’s differential fields version of Schanuel’s conjecture to semiabelian varieties. There is a purely algebraic corollary,
the “Weak CIT” for semiabelian varieties, which concerns the intersections of algebraic subgroups with algebraic varieties. 相似文献
18.
Takashi Agoh 《manuscripta mathematica》1995,87(1):501-510
In this paper we shall investigate Giuga’s conjecture which asserts an interesting characterization of prime numbers, just
as Wilson’s Theorem. Some variations and consequences of the Giuga congruence are discussed by means of Bernoulli numbers.
In addition, we shall study various quotients relating to the integers satisfying the Giuga congruence.
To the memory of Suzuko Koshiba-Takamiya
This article was processed by the author using the LATEX style filecljourl from Springer-Verlag 相似文献
19.
Yu. L. Ershov 《Siberian Mathematical Journal》2011,52(5):836-839
The explicit form is given of the separants of the polynomials of the author’s previous article [1]. This entails clarification
of the main theorem of [1]. 相似文献
20.
A. Vishik 《manuscripta mathematica》2007,122(3):365-374
In this article we study the sufficient conditions for the k̅-defined element of the Chow group of a smooth variety to be
k-rational (defined over k). For 0-cycles this question was addressed earlier. Our methods work for cycles of arbitrary dimension. We show that it is
sufficient to check this property over the generic point of a quadric of sufficiently large dimension. Among the applications
one should mention the uniform construction of fields with all known u-invariants. 相似文献