共查询到20条相似文献,搜索用时 671 毫秒
1.
The “Projective Rank” of a compact connected irreducible Hermitian symmetric space M has been defined as the maximal complex dimension of the compact totally geodesic complex submanifolds having positive holomorphic bisectional curvature with the induced K?hler metric. We present a geometric way to compute this
invariant for the space M based on ideas developed in [1], [13] and [14]. As a consequence we obtain the following inequality relating the Projective Rank,
the usual rank, and the 2-number (which is known to be equal to the Euler-Poincare characteristic in these spaces).
Received: 6 June 2000 / Revised version: 6 August 2001 / Published online: 4 April 2002 相似文献
2.
The “Projective Rank” of a compact connected irreducible Hermitian symmetric space M has been defined as the maximal complex dimension of the compact totally geodesic complex submanifolds having positive holomorphic bisectional curvature with the induced K?hler metric. We present a geometric way to compute this
invariant for the space M based on ideas developed in [1], [13] and [14]. As a consequence we obtain the following inequality relating the Projective Rank, Pr(M), the usual rank,rk(M), and the 2-number # (which is known to be equal to the Euler-Poincare characteristic in these spaces).
Received: 6 June 2000 / Published online: 1 February 2002 相似文献
3.
Yongdo Lim 《Mathematische Annalen》2000,316(2):379-389
Let V be a simple Euclidean Jordan algebra with an associative inner product and let be the corresponding symmetric cone. Let be the compact symmetric space of all primitive idempotents of V. We show that the function s(a,b) defined by
is a (the automorphism group of )-invariant complete metric on and it coincides with a natural Finsler distance on We also show that the metric s(a,b) (strictly) contracts any (strict) conformal compression of .
Received: 24 May 1999 / in final form: 15 March 1999 相似文献
4.
Ulrich Clarenz Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》2001,12(1):85-107
We consider parametric variational double integrals with elliptic Lagrangians F depending on the surface normal and prove a compactness theorem for -critical immersions. As a key ingredient for the relevant a priori estimates we use F. Sauvigny's F-conformal parameters adapted to the parametric integrand F. As a by-product of our analysis we obtain an isoperimetric inequality for -critical immersions generalizing the classical isoperimetric inequality for minimal surfaces.
Received November 19, 1999 / Accepted February 4, 2000 / Published online July 20, 2000 相似文献
5.
We prove uniform decay estimates at infinity for solutions 0?u∈Lp of the semilinear elliptic inequality Δu+auσ+bu?0, a,b?0, σ?1, in the presence of a Sobolev inequality (with potential term). This gives a unified point of view in the investigation of different geometric questions. In particular, we present applications to the study of the topology at infinity of parallel mean curvature submanifolds, to the non-compact Yamabe problem, and to estimate the decay rate of the traceless Ricci tensor of conformally flat manifolds. 相似文献
6.
Kong‐Ming Chong 《International Journal of Mathematical Education in Science & Technology》2013,44(6):653-654
This article gives a simple inductive proof of the following classical inequality connecting the arithmetic and geometric means of the n positive quantities a 1, a 2,......an : by using the fact that the geometric mean of the n — 1 numbers is the same as that of a 1, a 2,......an : An inductive procedure is then applicable to proving the inequality from the case n — 1 to the case n by repeated applications of a simple inequality involving two pairs of positive numbers with the same product. 相似文献
7.
Jorge Lauret 《manuscripta mathematica》1999,99(3):287-309
For each compact Lie algebra ? and each real representation V of ? we consider a two-step nilpotent Lie group N(?,V), endowed with a natural left-invariant riemannian metric. The homogeneous nilmanifolds so obtained are precisely those
which are naturally reductive. We study some geometric aspects of these manifolds, finding many parallels with H-type groups. We also obtain, within the class of manifolds N(?,V), the first examples of non-weakly symmetric, naturally reductive spaces and new examples of non-commutative naturally reductive
spaces.
Received: 16 September 1998 / Revised version: 24 February 1999 相似文献
8.
J. Sándor 《Aequationes Mathematicae》1990,40(1):261-270
Summary Leta, b > 0 be positive real numbers. The identric meanI(a, b) of a andb is defined byI = I(a, b) = (1/e)(b
b
/a
a
)
1/(b–a)
, fora b, I(a, a) = a; while the logarithmic meanL(a, b) ofa andb isL = L(a, b) = (b – a)/(logb – loga), fora b, L(a, a) = a. Let us denote the arithmetic mean ofa andb byA = A(a, b) = (a + b)/2 and the geometric mean byG =G(a, b) =
. In this paper we obtain some improvements of known results and new inequalities containing the identric and logarithmic means. The material is divided into six parts. Section 1 contains a review of the most important results which are known for the above means. In Section 2 we prove an inequality which leads to some improvements of known inequalities. Section 3 gives an application of monotonic functions having a logarithmically convex (or concave) inverse function. Section 4 works with the logarithm ofI(a, b), while Section 5 is based on the integral representation of means and related integral inequalities. Finally, Section 6 suggests a new mean and certain generalizations of the identric and logarithmic means. 相似文献
9.
Horatio Quadjovie 《Bulletin des Sciences Mathématiques》2004,128(6):447-466
A rotationally symmetric, compact, oriented, connected, uniformly convex hypersurface M0 of , with boundary ∂M0 in a rotationally symmetric cone S, is evolving under volume-preserving mean curvature flow. Then for n?2, we obtain gradient and curvature estimates, leading to long-time existence of the flow, and convergence to a part of a round sphere. 相似文献
10.
In correspondence with the manifolds of quasi-constant sectional curvature defined (cf [5], [9]) in the Riemannian context,
we introduce in the K?hlerian framework the geometric notion of quasi-constant holomorphic sectional curvature. Some characterizations
and properties are given. We obtain necessary and sufficient conditions for these manifolds to be locally symmetric, Ricci
or Bochner flat, K?hler η-Einstein or K?hler-Einstein, etc. The characteristic classes are studied at the end and some examples are provided throughout.
相似文献
11.
Monique Laurent 《Combinatorica》2001,21(4):543-570
Given a graph G on n nodes, let denote the cone consisting of the positive semidefinite matrices (with real or complex entries) having a zero entry at every off-diagonal position corresponding to a non edge of
G. Then, the sparsity order of G is defined as the maximum rank of a matrix lying on an extreme ray of the cone .
It is known that the graphs with sparsity order 1 are the chordal graphs and a characterization of the graphs with sparsity
order 2 is conjectured in [1] in the real case. We show in this paper the validity of this conjecture. Moreover, we characterize
the graphs with sparsity order 2 in the complex case and we give a decomposition result for the graphs with sparsity order
in both real and complex cases. As an application, these graphs can be recognized in polynomial time.
We also indicate how an inequality from [17] relating the sparsity order of a graph and its minimum fill-in can be derived
from a result concerning the dimension of the faces of the cone .
Received August 31, 1998/Revised April 26, 2000 相似文献
12.
J. A. Carrillo A. Jüngel P. A. Markowich G. Toscani A. Unterreiter 《Monatshefte für Mathematik》2001,133(1):1-82
We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems
with confinement by a uniformly convex potential, 2) unconfined scalar equations and 3) unconfined systems. In particular
we are interested in the rate of decay to equilibrium or self-similar solutions. The main analytical tool is based on the
analysis of the entropy dissipation. In the scalar case this is done by proving decay of the entropy dissipation rate and
bootstrapping back to show convergence of the relative entropy to zero. As by-product, this approach gives generalized Sobolev-inequalities,
which interpolate between the Gross logarithmic Sobolev inequality and the classical Sobolev inequality. The time decay of
the solutions of the degenerate systems is analyzed by means of a generalisation of the Nash inequality. Porous media, fast
diffusion, p-Laplace and energy transport systems are included in the considered class of problems. A generalized Csiszár–Kullback inequality
allows for an estimation of the decay to equilibrium in terms of the relative entropy.
(Received 11 October 2000; in revised form 13 March 2001) 相似文献
13.
14.
Barvinok 《Foundations of Computational Mathematics》2008,2(4):393-412
Abstract. Let G be a compact group acting in a real vector space V . We obtain a number of inequalities relating the L
∞ norm of a matrix element of the representation of G with its L
2k
norm for a positive integer k . As an application, we obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial
over the unit sphere (in which case G is the orthogonal group) and for the assignment problem of degree d , a hard problem of combinatorial optimization generalizing the quadratic assignment problem (in which case G is the symmetric group). 相似文献
15.
16.
Nathalie Eisenbaum 《Probability Theory and Related Fields》1997,107(4):527-535
Summary. At time t, the most visited site of a linear Brownian motion is defined as the point which realises the supremum of the local times
at time t. Let V be the time indexed process of the most visited sites by a linear Brownian motion. We show that every value is polar for
V. Those results are extended from Brownian motion to symmetric stable processes, and then to the absolute value of a symmetric
stable process.
Received: 1 March 1996 / In revised form: 17 October 1996 相似文献
17.
18.
Francesca Alessio Louis Jeanjean Piero Montecchiari 《Calculus of Variations and Partial Differential Equations》2000,11(2):177-202
We consider a class of non autonomous Allen-Cahn equations
where is a multiple-well potential and is a periodic, positive, non-constant function. We look for solutions to (0.1) having uniform limits as corresponding to minima of W. We show, via variational methods, that under a nondegeneracy condition on the set of heteroclinic solutions of the associated
ordinary differential equation
the equation (0.1) has solutions which depends on both the variables x andy. In contrast, when a is constant such nondegeneracy condition is not satisfied and all such solutions are known to depend only on x.
Received April 16, 1999 / Accepted October 1, 1999 / Published online June 28, 2000 相似文献
19.
In this paper, we are concerned with the global singularity structures of weak solutions to 4-D semilinear dispersive wave
equations whose initial data are chosen to be discontinuous on the unit sphere. Combining Strichartz's inequality with the
commutator argument techniques, we show that the weak solutions are C2−regular away from the focusing cone surface |x|=|t−1| and the outgoing cone surface |x|=t+1.
This research was supported by the National Natural Science Foundation of China and the Doctoral Foundation of NEM of China. 相似文献
20.
Given two disjoint subsets T
1 and
T
2 of
nodes in an undirected 3-connected graph G = (V, E) with node set
V and arc set
E, where
and
are even numbers, we
show that V can be
partitioned into two sets V
1 and
V
2
such that the graphs induced by V
1 and
V
2 are
both connected and
holds for each
j = 1,2. Such a partition can
be found in
time. Our proof relies
on geometric arguments. We define a new type of convex
embedding of k-connected
graphs into real space R
k-1 and prove that for
k = 3 such an embedding
always exists.
1 A preliminary version
of this paper with title Bisecting Two Subsets in 3-Connected
Graphs appeared in the Proceedings of the 10th Annual
International Symposium on Algorithms and Computation, ISAAC
99, (A. Aggarwal, C. P. Rangan, eds.), Springer LNCS 1741,
425–434, 1999. 相似文献