共查询到20条相似文献,搜索用时 31 毫秒
1.
Christopher Hammond 《Mathematische Zeitschrift》2010,266(2):285-288
Let Ω be a domain in ${\mathbb{C}^{2}}Let Ω be a domain in
\mathbbC2{\mathbb{C}^{2}}, and let
p: [(W)\tilde]? \mathbbC2{\pi: \tilde{\Omega}\rightarrow \mathbb{C}^{2}} be its envelope of holomorphy. Also let W¢=p([(W)\tilde]){\Omega'=\pi(\tilde{\Omega})} with
i: W\hookrightarrow W¢{i: \Omega \hookrightarrow \Omega'} the inclusion. We prove the following: if the induced map on fundamental groups i*:p1(W) ? p1(W¢){i_{*}:\pi_{1}(\Omega) \rightarrow \pi_{1}(\Omega')} is a surjection, and if π is a covering map, then Ω has a schlicht envelope of holomorphy. We then relate this to earlier
work of Fornaess and Zame. 相似文献
2.
In this paper, we mainly study polynomial generalized Vekua-type equation _boxclose)w=0{p(\mathcal{D})w=0} and polynomial generalized Bers–Vekua equation p(D)w=0{p(\mathcal{\underline{D}})w=0} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}} where D{\mathcal{D}} and D{\mathcal{\underline{D}}} mean generalized Vekua-type operator and generalized Bers–Vekua operator, respectively. Using Clifford algebra, we obtain
the Fischer-type decomposition theorems for the solutions to these equations including
(D-l)kw=0,(D-l)kw=0(k ? \mathbbN){\left(\mathcal{D}-\lambda\right)^{k}w=0,\left(\mathcal {\underline{D}}-\lambda\right)^{k}w=0\left(k\in\mathbb{N}\right)} with complex parameter λ as special cases, which derive the Almansi-type decomposition theorems for iterated generalized
Bers–Vekua equation and polynomial generalized Cauchy–Riemann equation defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}. Making use of the decomposition theorems we give the solutions to polynomial generalized Bers–Vekua equation defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}} under some conditions. Furthermore we discuss inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}, and develop the structure of the solutions to inhomogeneous polynomial generalized Bers–Vekua equation p(D)w=v{p(\mathcal{\underline{D}})w=v} defined in
W ì \mathbbRn+1{\Omega\subset\mathbb{R}^{n+1}}. 相似文献
3.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
4.
Let M be
(2n-1)\mathbbCP2#2n[`(\mathbbCP)]2(2n-1)\mathbb{CP}^{2}\#2n\overline{\mathbb{CP}}{}^{2} for any integer n≥1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is
\mathbbCP2#4[`(\mathbbCP)]2\mathbb{CP}{}^{2}\#4\overline {\mathbb{CP}}{}^{2} or
3\mathbbCP2#k[`(\mathbbCP)]23\mathbb{CP}{}^{2}\#k\overline{\mathbb{CP}}{}^{2} for k=6,8,10. 相似文献
5.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
6.
M. F. Betta F. Chiacchio A. Ferone 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):37-52
We find some optimal estimates for the first eigenfunction of a class of elliptic equations whose prototype is
- ( guxi )xi = lgu \textin W ì \mathbbRn - {\left( {\gamma u_{{x_{i} }} } \right)}_{{x_{i} }} = \lambda \gamma u\,{\text{in}}\,\Omega \subset \mathbb{R}^{n}
with Dirichlet boundary condition, where γ is the normalized Gaussian function in
\mathbbRn \mathbb{R}^{n}
. To this aim we make use of the Gaussian symmetrization which transforms a domain into an half-space with the same Gaussian
measure. The main tools we use are the properties of the weighted rearrangements and in particular the isoperimetric inequality
with respect to Gaussian measure. 相似文献
7.
Nam Q. Le 《Geometriae Dedicata》2011,151(1):361-371
Consider a family of smooth immersions
F(·,t) : Mn? \mathbbRn+1{F(\cdot,t)\,:\,{M^n\to \mathbb{R}^{n+1}}} of closed hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}} moving by the mean curvature flow
\frac?F(p,t)?t = -H(p,t)·n(p,t){\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)}, for t ? [0,T){t\in [0,T)}. We show that at the first singular time of the mean curvature flow, certain subcritical quantities concerning the second
fundamental form, for example
ò0tòMs\frac|A|n + 2 log (2 + |A|) dmds,{\int_{0}^{t}\int_{M_{s}}\frac{{\vert{\it A}\vert}^{n + 2}}{ log (2 + {\vert{\it A}\vert})}} d\mu ds, blow up. Our result is a log improvement of recent results of Le-Sesum, Xu-Ye-Zhao where the scaling invariant quantities
were considered. 相似文献
8.
M. Fuchs 《Journal of Mathematical Sciences》2011,175(3):375-389
We consider local minimizers
u:\mathbbR2 é W? \mathbbRM u:{\mathbb{R}^2} \supset \Omega \to {\mathbb{R}^M} of the variational integral
òW H( ?u )dx \int\limits_\Omega {H\left( {\nabla u} \right)dx} 相似文献
9.
N. A. Veniaminov 《Journal of Mathematical Sciences》2010,169(1):46-63
We study the asymptotics of the spectrum of the Maxwell operator M in a bounded Lipschitz domain
W ì \mathbbR3 \Omega \subset {\mathbb{R}^3} under the condition of the perfect conductivity of the boundary ∂Ω. We obtain the following estimate for the remainder in
the Weyl asymptotic expansion of the counting function N(λ,M) of positive eigenvalues of the Maxwell operator M:
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