共查询到20条相似文献,搜索用时 15 毫秒
1.
Pak Tung Ho 《Mathematische Annalen》2010,348(2):319-332
Suppose (N n , g) is an n-dimensional Riemannian manifold with a given smooth measure m. The P-scalar curvature is defined as ${P(g)=R^m_\infty(g)=R(g)-2\Delta_g{\rm log}\,\phi-|\nabla_g{\rm log}\,\phi|_g^2}Suppose (N
n
, g) is an n-dimensional Riemannian manifold with a given smooth measure m. The P-scalar curvature is defined as P(g)=Rm¥(g)=R(g)-2Dglog f-|?glog f|g2{P(g)=R^m_\infty(g)=R(g)-2\Delta_g{\rm log}\,\phi-|\nabla_g{\rm log}\,\phi|_g^2}, where dm=f dvol(g){dm=\phi\,dvol(g)} and R(g) is the scalar curvature of (N
n
, g). In this paper, under a technical assumption on f{\phi}, we prove that f{\phi}-stable minimal oriented hypersurface in the three-dimensional manifold with nonnegative P-scalar curvature must be conformally equivalent to either the complex plane
\mathbbC{\mathbb{C}} or the cylinder
\mathbbR×\mathbbS1{\mathbb{R}\times\mathbb{S}^1}. 相似文献
2.
Let
W í \Bbb C\Omega \subseteq {\Bbb C}
be a simply connected domain in
\Bbb C{\Bbb C}
, such that
{¥} è[ \Bbb C \[`(W)]]\{\infty\} \cup [ {\Bbb C} \setminus \bar{\Omega}]
is connected. If g is holomorphic in Ω and every derivative of g extends continuously on
[`(W)]\bar{\Omega}
, then we write g ∈ A∞ (Ω). For g ∈ A∞ (Ω) and
z ? [`(W)]\zeta \in \bar{\Omega}
we denote
SN (g,z)(z) = ?Nl=0\fracg(l) (z)l ! (z-z)lS_N (g,\zeta )(z)= \sum^{N}_{l=0}\frac{g^{(l)} (\zeta )}{l !} (z-\zeta )^l
. We prove the existence of a function f ∈ A∞(Ω), such that the following hold:
相似文献
i) | There exists a strictly increasing sequence μn ∈ {0, 1, 2, …}, n = 1, 2, …, such that, for every pair of compact sets Γ, Δ ⊂ [`(W)]\bar{\Omega} and every l ∈ {0, 1, 2, …} we have supz ? G supw ? D \frac?l?wl Smn ( f,z) (w)-f(l)(w) ? 0, as n ? + ¥ and\sup_{\zeta \in \Gamma} \sup_{w \in \Delta} \frac{\partial^l}{\partial w^l} S_{\mu_ n} (\,f,\zeta) (w)-f^{(l)}(w) \rightarrow 0, \hskip 7.8pt {\rm as}\,n \rightarrow + \infty \quad {\rm and} |
ii) | For every compact set K ì \Bbb CK \subset {\Bbb C} with K?[`(W)] = ?K\cap \bar{\Omega} =\emptyset and Kc connected and every function h: K? \Bbb Ch: K\rightarrow {\Bbb C} continuous on K and holomorphic in K0, there exists a subsequence { m¢n }¥n=1\{ \mu^\prime _n \}^{\infty}_{n=1} of {mn }¥n=1\{\mu_n \}^{\infty}_{n=1} , such that, for every compact set L ì [`(W)]L \subset \bar{\Omega} we have supz ? L supz ? K Sm¢n ( f,z)(z)-h(z) ? 0, as n? + ¥.\sup_{\zeta \in L} \sup_{z\in K} S_{\mu^\prime _n} (\,f,\zeta )(z)-h(z) \rightarrow 0, \hskip 7.8pt {\rm as} \, n\rightarrow + \infty . |
3.
For a locally compact group G, we present some characterizations for f{\phi}-contractibility of the Lebesgue–Fourier algebra LA(G){\mathcal{L}A(G)} endowed with convolution or pointwise product. 相似文献
4.
For a graph G of order |V(G)| = n and a real-valued mapping
f:V(G)?\mathbbR{f:V(G)\rightarrow\mathbb{R}}, if S ì V(G){S\subset V(G)} then f(S)=?w ? S f(w){f(S)=\sum_{w\in S} f(w)} is called the weight of S under f. The closed (respectively, open) neighborhood sum of f is the maximum weight of a closed (respectively, open) neighborhood under f, that is, NS[f]=max{f(N[v])|v ? V(G)}{NS[f]={\rm max}\{f(N[v])|v \in V(G)\}} and NS(f)=max{f(N(v))|v ? V(G)}{NS(f)={\rm max}\{f(N(v))|v \in V(G)\}}. The closed (respectively, open) lower neighborhood sum of f is the minimum weight of a closed (respectively, open) neighborhood under f, that is, NS-[f]=min{f(N[v])|v ? V(G)}{NS^{-}[f]={\rm min}\{f(N[v])|v\in V(G)\}} and NS-(f)=min{f(N(v))|v ? V(G)}{NS^{-}(f)={\rm min}\{f(N(v))|v\in V(G)\}}. For
W ì \mathbbR{W\subset \mathbb{R}}, the closed and open neighborhood sum parameters are NSW[G]=min{NS[f]|f:V(G)? W{NS_W[G]={\rm min}\{NS[f]|f:V(G)\rightarrow W} is a bijection} and NSW(G)=min{NS(f)|f:V(G)? W{NS_W(G)={\rm min}\{NS(f)|f:V(G)\rightarrow W} is a bijection}. The lower neighbor sum parameters are NS-W[G]=maxNS-[f]|f:V(G)? W{NS^{-}_W[G]={\rm max}NS^{-}[f]|f:V(G)\rightarrow W} is a bijection} and NS-W(G)=maxNS-(f)|f:V(G)? W{NS^{-}_W(G)={\rm max}NS^{-}(f)|f:V(G)\rightarrow W} is a bijection}. For bijections f:V(G)? {1,2,?,n}{f:V(G)\rightarrow \{1,2,\ldots,n\}} we consider the parameters NS[G], NS(G), NS
−[G] and NS
−(G), as well as two parameters minimizing the maximum difference in neighborhood sums. 相似文献
5.
Straightening and bounded cohomology of hyperbolic groups 总被引:2,自引:0,他引:2
I. Mineyev 《Geometric And Functional Analysis》2001,11(4):807-839
It was stated by M. Gromov [Gr2] that, for any hyperbolic group G, the map from bounded cohomology Hnb(G,\Bbb R) H^n_b(G,{\Bbb R}) to Hn(G,\Bbb R) H^n(G,{\Bbb R}) induced by inclusion is surjective for n 3 2 n \ge 2 . We introduce a homological analogue of straightening simplices, which works for any hyperbolic group. This implies that the map Hnb(G,V) ? Hn(G,V) H^n_b(G,V) \to H^n(G,V) is surjective for n 3 2 n \ge 2 when V is any bounded \Bbb QG {\Bbb Q}G -module and when V is any finitely generated abelian group. 相似文献
6.
G. Kutyniok 《Archiv der Mathematik》2002,78(2):135-144
Let
r\mathbbR \rho_{\mathbb{R}} be the classical Schrödinger representation of the Heisenberg group and let L \Lambda be a finite subset of
\mathbbR ×\mathbbR \mathbb{R} \times \mathbb{R} . The question of when the set of functions
{t ? e2 pi y t f(t + x) = (r\mathbbR(x, y, 1) f)(t) : (x, y) ? L} \{t \mapsto e^{2 \pi i y t} f(t + x) = (\rho_{\mathbb{R}}(x, y, 1) f)(t) : (x, y) \in \Lambda\} is linearly independent for all
f ? L2(\mathbbR), f 1 0 f \in L^2(\mathbb{R}), f \neq 0 , arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset L \Lambda of G ×[^(G)] G \times \widehat{G} and rG \rho_G the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {rG (x, w, 1)f : (x, w) ? L} \{\rho_G (x, w, 1)f : (x, w) \in \Lambda\} to be linearly independent for all f ? L2(G), f 1 0 f \in L^2(G), f \neq 0 . 相似文献
7.
Wojciech Jaworski 《Monatshefte für Mathematik》2008,336(4):135-144
Given a locally compact group G, let
J(G){\cal J}(G)
denote the set of closed left ideals in L
1(G), of the form J
μ = [L1(G) * (δ
e
− μ)]−, where μ is a probability measure on G. Let
Jd(G)={\cal J}_d(G)=
{Jm;m is discrete}\{J_{\mu};\mu\ {\rm is discrete}\}
,
Ja(G)={Jm;m is absolutely continuous}{\cal J}_a(G)=\{J_{\mu};\mu\ {\rm is absolutely continuous}\}
. When G is a second countable [SIN] group, we prove that
J(G)=Jd(G){\cal J}(G)={\cal J}_d(G)
and that
Ja(G){\cal J}_a(G)
, being a proper subset of
J(G){\cal J}(G)
when G is nondiscrete, contains every maximal element of
J(G){\cal J}(G)
. Some results concerning the ideals J
μ in general locally compact second countable groups are also obtained. 相似文献
8.
Harald Grobner 《Monatshefte für Mathematik》2010,139(1):335-340
Let
G/\mathbb Q{G/\mathbb Q} be the simple algebraic group Sp(n, 1) and G = G(N){\Gamma=\Gamma(N)} a principal congruence subgroup of level N ≥ 3. Denote by K a maximal compact subgroup of the real Lie group
G(\mathbb R){G(\mathbb R)} . Then a double quotient
G\G(\mathbb R)/K{\Gamma\backslash G(\mathbb R)/K} is called an arithmetically defined, quaternionic hyperbolic n-manifold. In this paper we give an explicit growth condition for the dimension of cuspidal cohomology
H2ncusp(G\G(\mathbb R)/K,E){H^{2n}_{cusp}(\Gamma\backslash G(\mathbb R)/K,E)} in terms of the underlying arithmetic structure of G and certain values of zeta-functions. These results rely on the work of Arakawa (Automorphic Forms of Several Variables:
Taniguchi Symposium, Katata, 1983, eds. I. Satake and Y. Morita (Birkh?user, Boston), pp. 1–48, 1984). 相似文献
9.
10.
B. A. Khudaigulyev 《Ukrainian Mathematical Journal》2011,62(12):1989-1999
We consider the following problem of finding a nonnegative function u(x) in a ball B = B(O, R) ⊂ R
n
, n ≥ 3:
- Du = V(x)u, u| ?B = f(x), - \Delta u = V(x)u,\,\,\,\,\,u\left| {_{\partial B} = \phi (x),} \right. 相似文献
11.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
\Bbb C{\Bbb C}
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
Cn(W,P) := supf ? A(W,P)supz ? W\frac|f(n)(z)| R(f(z),P)n! (R(z,W))nC_n(\Omega,\Pi)\,:=\,\sup_{f\in A(\Omega,\Pi)}\sup_{z\in \Omega}\frac{\vert f^{(n)}(z)\vert\,R(f(z),\Pi)}{n!\,(R(z,\Omega))^n}
are finite for all
n ? \Bbb N{n \in {\Bbb N}}
if and only if ∂Ω and ∂Π do not contain isolated points. 相似文献
12.
Let F ì PG \mathcal{F} \subset {\mathcal{P}_G} be a left-invariant lower family of subsets of a group G. A subset A ⊂ G is called F \mathcal{F} -thin if xA ?yA ? F xA \cap yA \in \mathcal{F} for any distinct elements x, y ∈ G. The family of all F \mathcal{F} -thin subsets of G is denoted by t( F ) \tau \left( \mathcal{F} \right) . If t( F ) = F \tau \left( \mathcal{F} \right) = \mathcal{F} , then F \mathcal{F} is called thin-complete. The thin-completion t*( F ) {\tau^*}\left( \mathcal{F} \right) of F \mathcal{F} is the smallest thin-complete subfamily of PG {\mathcal{P}_G} that contains F \mathcal{F} . Answering questions of Lutsenko and Protasov, we prove that a set A ⊂ G belongs to τ*(G) if and only if, for any sequence (g
n
)
n∈ω
of nonzero elements of G, there is n ∈ ω such that
|