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1.
We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S n+1 satisfying Sf 4 f_3~2 ≤ 1/n S~3 , where S is the squared norm of the second fundamental form of M, and f_k =sum λ_i~k from i and λ_i (1 ≤ i ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n + δ(n), then S ≡ n, i.e., M is one of the Clifford torus S~k ((k/n)~1/2 ) ×S~... 相似文献
2.
James East 《Semigroup Forum》2010,81(2):357-379
The (full) transformation semigroup Tn\mathcal{T}_{n} is the semigroup of all functions from the finite set {1,…,n} to itself, under the operation of composition. The symmetric group Sn í Tn{\mathcal{S}_{n}\subseteq \mathcal{T}_{n}} is the group of all permutations on {1,…,n} and is the group of units of Tn\mathcal{T}_{n}. The complement Tn\Sn\mathcal{T}_{n}\setminus \mathcal{S}_{n} is a subsemigroup (indeed an ideal) of Tn\mathcal{T}_{n}. In this article we give a presentation, in terms of generators and relations, for Tn\Sn\mathcal{T}_{n}\setminus \mathcal{S}_{n}, the so-called singular part of Tn\mathcal{T}_{n}. 相似文献
3.
Hai-Ping Fu 《Proceedings Mathematical Sciences》2010,120(4):457-464
Let M
n
(n ≥ 3) be an n-dimensional complete immersed $
\frac{{n - 2}}
{n}
$
\frac{{n - 2}}
{n}
-super-stable minimal submanifold in an (n + p)-dimensional Euclidean space ℝ
n+p
with flat normal bundle. We prove that if the second fundamental form of M satisfies some decay conditions, then M is an affine plane or a catenoid in some Euclidean subspace. 相似文献
4.
Thomas Hasanis Andreas Savas-Halilaj Theodoros Vlachos 《Monatshefte für Mathematik》2005,71(1):301-305
In this paper we investigate complete minimal hypersurfaces
f : Mn? \Bbb Sn+1f : M^{n}\rightarrow {\Bbb S}^{n+1}
with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(Mn) is a minimal Clifford torus. 相似文献
5.
We estimate from below the isoperimetric profile of
S2 ×\mathbb R2{S^2 \times {\mathbb R}^2} and use this information to obtain lower bounds for the Yamabe constant of
S2 ×\mathbb R2{S^2 \times {\mathbb R}^2} . This provides a lower bound for the Yamabe invariants of products S
2 × M
2 for any closed Riemann surface M. Explicitly we show that Y (S
2 × M
2) > (2/3)Y(S
4). 相似文献
6.
We consider the space M(n,m)\mathcal{M}(n,m) of ordered m-tuples of distinct points in the boundary of complex hyperbolic n-space,
H\mathbbCn\mathbf{H}_{\mathbb{C}}^{n}, up to its holomorphic isometry group PU(n,1). An important problem in complex hyperbolic geometry is to construct and describe the moduli space for M(n,m)\mathcal{M}(n,m). In particular, this is motivated by the study of the deformation space of complex hyperbolic groups generated by loxodromic
elements. In the present paper, we give the complete solution to this problem. 相似文献
7.
We study compact minimal hypersurfaces Mn in Sn+1S^{n+1} with two distinct principal curvatures and prove that if the squared norm S of the second fundamental form of Mn satisfies S \geqq nS \geqq n, then S o nS \equiv n and Mn is a minimal Clifford torus. 相似文献
8.
Thomas Hasanis Andreas Savas-Halilaj Theodoros Vlachos 《Monatshefte für Mathematik》2005,145(4):301-305
In this paper we investigate complete minimal hypersurfaces
with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(Mn) is a minimal Clifford torus. 相似文献
9.
We complete the study of the supersingular locus Mss\mathcal{M}^{\mathrm{ss}} in the fiber at p of a Shimura variety attached to a unitary similitude group GU(1,n−1) over ℚ in the case that p is inert. This was started by the first author in Can. J. Math. 62, 668–720 (2010) where complete results were obtained for n=2,3. The supersingular locus Mss\mathcal{M}^{\mathrm{ss}} is uniformized by a formal scheme N\mathcal{N} which is a moduli space of so-called unitary p-divisible groups. It depends on the choice of a unitary isocrystal N. We define a stratification of N\mathcal{N} indexed by vertices of the Bruhat-Tits building attached to the reductive group of automorphisms of N. We show that the combinatorial behavior of this stratification is given by the simplicial structure of the building. The
closures of the strata (and in particular the irreducible components of Nred\mathcal{N}_{\mathrm{red}}) are identified with (generalized) Deligne-Lusztig varieties. We show that the Bruhat-Tits stratification is a refinement
of the Ekedahl-Oort stratification and also relate the Ekedahl-Oort strata to Deligne-Lusztig varieties. We deduce that Mss\mathcal{M}^{\mathrm{ss}} is locally a complete intersection, that its irreducible components and each Ekedahl-Oort stratum in every irreducible component
is isomorphic to a Deligne-Lusztig variety, and give formulas for the number of irreducible components of every Ekedahl-Oort
stratum of Mss\mathcal{M}^{\mathrm{ss}}. 相似文献
10.
V. G. Puzarenko 《Siberian Advances in Mathematics》2010,20(2):128-154
We study some properties of a $
\mathfrak{c}
$
\mathfrak{c}
-universal semilattice $
\mathfrak{A}
$
\mathfrak{A}
with the cardinality of the continuum, i.e., of an upper semilattice of m-degrees. In particular, it is shown that the quotient semilattice of such a semilattice modulo any countable ideal will be
also $
\mathfrak{c}
$
\mathfrak{c}
-universal. In addition, there exists an isomorphism
$
\mathfrak{A}
$
\mathfrak{A}
such that $
{\mathfrak{A} \mathord{\left/
{\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right.
\kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}}
$
{\mathfrak{A} \mathord{\left/
{\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right.
\kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}}
will be also $
\mathfrak{c}
$
\mathfrak{c}
-universal. Furthermore, a property of the group of its automorphisms is obtained. To study properties of this semilattice,
the technique and methods of admissible sets are used. More exactly, it is shown that the semilattice of mΣ-degrees $
L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)}
$
L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)}
on the hereditarily finite superstructure $
\mathbb{H}\mathbb{F}
$
\mathbb{H}\mathbb{F}
(S) over a countable set S will be a $
\mathfrak{c}
$
\mathfrak{c}
-universal semilattice with the cardinality of the continuum. 相似文献
11.
Yi Fang 《Archiv der Mathematik》1999,72(6):473-480
12.
Marcos M. Alexandrino 《Geometriae Dedicata》2010,149(1):397-416
Let F{\mathcal{F}} be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F{\mathcal{F}} we construct a regular Riemannian foliation [^(F)]{\hat{\mathcal{F}}} on a compact Riemannian manifold [^(M)]{\hat{M}} and a desingularization map [^(r)]:[^(M)]? M{\hat{\rho}:\hat{M}\rightarrow M} that projects leaves of [^(F)]{\hat{\mathcal{F}}} into leaves of F{\mathcal{F}}. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose
leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F{\mathcal{F}} are compact, then, for each small ${\epsilon >0 }${\epsilon >0 }, we can find [^(M)]{\hat{M}} and [^(F)]{\hat{\mathcal{F}}} so that the desingularization map induces an e{\epsilon}-isometry between M/F{M/\mathcal{F}} and [^(M)]/[^(F)]{\hat{M}/\hat{\mathcal{F}}}. This implies in particular that the space of leaves M/F{M/\mathcal{F}} is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {([^(M)]n/[^(F)]n)}{\{(\hat{M}_{n}/\hat{\mathcal{F}}_{n})\}}. 相似文献
13.
Heleno Cunha Francisco Dutenhefner Nikolay Gusevskii Rafael Santos Thebaldi 《Journal of Geometric Analysis》2012,22(2):295-319
We consider the space M\mathcal{M} of ordered m-tuples of distinct complex geodesics in complex hyperbolic 2-space,
H\mathbbC2{\rm\bf H}_{\mathbb{C}}^{2}, up to its holomorphic isometry group PU(2,1). One of the important problems in complex hyperbolic geometry is to construct
and describe the moduli space for M\mathcal{M}. This is motivated by the study of the deformation space of groups generated by reflections in complex geodesics. In the
present paper, we give the complete solution to this problem. 相似文献
14.
Let R be a noetherian ring,
\mathfraka{\mathfrak{a}} an ideal of R, and M an R-module. We prove that for a finite module M, if
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is minimax for all i ≥ r ≥ 1, then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is artinian for i ≥ r. A local–global principle for minimax local cohomology modules is shown. If
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is coatomic for i ≤ r (M finite) then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is finite for i ≤ r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing
theorems are proved for local cohomology modules. 相似文献
15.
We prove that the symplectic group
Sp(2n,\mathbbZ){Sp(2n,\mathbb{Z})} and the mapping class group Mod
S
of a compact surface S satisfy the R
∞ property. We also show that B
n
(S), the full braid group on n-strings of a surface S, satisfies the R
∞ property in the cases where S is either the compact disk D, or the sphere S
2. This means that for any automorphism f{\phi} of G, where G is one of the above groups, the number of twisted f{\phi}-conjugacy classes is infinite. 相似文献
16.
Alexander N. Dranishnikov Yuli B. Rudyak 《Journal of Fixed Point Theory and Applications》2009,6(1):165-177
It follows from a theorem of Gromov that the stable systolic category catstsys M{\rm cat}_{\rm stsys} M of a closed manifold M is bounded from below by
cl\mathbbQ M{\rm cl}_{\mathbb{Q}} M, the rational cup-length of M [Ka07]. We study the inequality in the opposite direction. In particular, combining our results with Gromov’s theorem, we
prove the equality
catstsys M = cl\mathbbQ M{\rm cat}_{\rm stsys} M = {\rm cl}_{\mathbb{Q}} M for simply connected manifolds of dimension ≤ 7. 相似文献
17.
S. Reifferscheid 《Archiv der Mathematik》2000,75(3):164-172
Let \frak X, \frak F,\frak X\subseteqq \frak F\frak {X}, \frak {F},\frak {X}\subseteqq \frak {F}, be non-trivial Fitting classes of finite soluble groups such that G\frak XG_{\frak {X}} is an \frak X\frak {X}-injector of G for all G ? \frak FG\in \frak {F}. Then \frak X\frak {X} is called \frak F\frak {F}-normal. If \frak F=\frak Sp\frak {F}=\frak {S}_{\pi }, it is known that (1) \frak X\frak {X} is \frak F\frak {F}-normal precisely when \frak X*=\frak F*\frak {X}^{\ast }=\frak {F}^{\ast }, and consequently (2) \frak F í \frak X\frak N\frak {F}\subseteq \frak {X}\frak {N} implies \frak X*=\frak F*\frak {X}^{\ast }=\frak {F}^{\ast }, and (3) there is a unique smallest \frak F\frak {F}-normal Fitting class. These assertions are not true in general. We show that there are Fitting classes \frak F\not = \frak Sp\frak {F}\not =\frak {S}_{\pi } filling property (1), whence the classes \frak Sp\frak {S}_{\pi } are not characterized by satisfying (1). Furthermore we prove that (2) holds true for all Fitting classes \frak F\frak {F} satisfying a certain extension property with respect to wreath products although there could be an \frak F\frak {F}-normal Fitting class outside the Lockett section of \frak F\frak {F}. Lastly, we show that for the important cases \frak F=\frak Nn, n\geqq 2\frak {F}=\frak {N}^{n},\ n\geqq 2, and \frak F=\frak Sp1?\frak Spr, pi \frak {F}=\frak {S}_{p_{1}}\cdots \frak {S}_{p_{r}},\ p_{i} primes, there is a unique smallest \frak F\frak {F}-normal Fitting class, which we describe explicitly. 相似文献
18.
19.
This paper deals with a coupled system of fourth-order parabolic inequalities |u|t ≥ 2u + |v|q,|v|t ≥ 2v + |u|p in S = Rn × R+ with p,q > 1,n ≥ 1.A FujitaLiouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n4 ≤ max(ppq+11,pqq+11).Since the general maximum-comparison principle does not hold for the fourth-order problem,the authors use the test function method to get the global non-existence of nontrivial solutions. 相似文献
20.
We show that if A is a closed analytic subset of
\mathbbPn{\mathbb{P}^n} of pure codimension q then
Hi(\mathbbPn\ A,F){H^i(\mathbb{P}^n{\setminus} A,{\mathcal F})} are finite dimensional for every coherent algebraic sheaf F{{\mathcal F}} and every
i 3 n-[\fracn-1q]{i\geq n-\left[\frac{n-1}{q}\right]} . If
n-1 3 2q we show that Hn-2(\mathbbPn\ A,F)=0{n-1\geq 2q\,{\rm we show that}\, H^{n-2}(\mathbb{P}^n{\setminus} A,{\mathcal F})=0} . 相似文献