共查询到20条相似文献,搜索用时 10 毫秒
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Let G be the group ${{\rm SL}(2, \mathbb{R})}$ . For this group we prove a version of Schwartz’s theorem on spectral analysis for the group G. We find the sharp range of Lebesgue spaces L p (G) for which a smooth function is not mean periodic unless it is a cusp form. Failure of the Schwartz-like theorem is also proved when C ∞(G) is replaced by L p (G) with suitable p. We show that the last result is linked with the failure of the Wiener-tauberian theorem for G. 相似文献
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Francisco Martin Masaaki Umehara Kotaro Yamada 《Calculus of Variations and Partial Differential Equations》2009,36(1):119-139
We construct a simply connected complete bounded mean curvature one surface in the hyperbolic 3-space ${\mathcal {H}^3}$ . Such a surface in ${\mathcal {H}^3}$ can be lifted as a complete bounded null curve in ${\rm {SL}(2,\mathbb {C})}$ . Using a transformation between null curves in ${\mathbb {C}^3}$ and null curves in ${\rm {SL}(2,\mathbb {C})}$ , we are able to produce the first examples of complete bounded null curves in ${\mathbb {C}^3}$ . As an application, we can show the existence of a complete bounded minimal surface in ${\mathbb {R}^3}$ whose conjugate minimal surface is also bounded. Moreover, we can show the existence of a complete bounded immersed complex submanifold in ${\mathbb {C}^2}$ . 相似文献
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Oleg N. Karpenkov Anatoly M. Vershik 《Journal of Fixed Point Theory and Applications》2010,7(1):241-263
How to find “best rational approximations” of maximal commutative subgroups of \({GL(n,\mathbb{R})}\)? In this paper we specify this problem and make first steps in its study. It contains the classical problems of Diophantine and simultaneous approximation as particular subcases but in general is much wider. We prove estimates for n = 2 for both totally real and complex cases and give an algorithm to construct best approximations of a fixed size. In addition we introduce a relation between best approximations and sails of cones and interpret the result for totally real subgroups in geometric terms of sails. 相似文献
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Any continuous strictly monotonic function \({F : {{\mathbb R}^{{\geq}0} \to {\mathbb R}}}\) with F(0) = 0 and F(t) → ∞ for t → ∞ gives rise to a topological rotational spread of \({{\rm PG}\,(3,{\mathbb R})}\); this spread is non-regular, if F is not linear. The action of the group \({SO_3({\mathbb R})}\) on this spread yields a topological parallelism of \({{\rm PG}\,(3,{\mathbb R})}\). The article also contains a short investigation on rotational spreads. Moreover, we construct a parallelism P 72 of \({{\rm PG}\,(3,{\mathbb R})}\) which is composed of piecewise regular spreads each consisting of two segments which are tacked together along a common regulus. Using Klein’s correspondence of line geometry and the Thas–Walker construction we represent every parallel class of P 72 via two parallel half-lines being non-interior to a given sphere in \({{\mathbb R}^3}\). The parallelism P 72 contains exactly one regular spread, all other members of P 72 are piecewise regular spreads with two segments. However, P 72 is not topological. 相似文献
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The aim of this paper is to show that every 2-local superderivation on an associative superalgebra is a superderivation.
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In a precedent article we constructed various topological regular parallelisms of the real projective 3-space \({{\rm PG}(3, \mathbb{R})}\) via hyperflock determining line sets of \({{\rm PG}(5, \mathbb{R})}\) (see Betten and Riesinger in Mh Math 161:43–58, 2010). In the present paper we discuss for some of these parallelisms their automorphism groups consisting of all automorphic collineations and all automorphic dualities, especially we compute their group dimension. Thus we are able to present: (1) topological regular 5-dimensional parallelisms of \({{\rm PG}(3, \mathbb{R})}\) of group dimension 0, (2) topological regular 4-dimensional parallelisms of \({{\rm PG}(3, \mathbb{R})}\) of group dimension 0 or 1, (3) topological regular 3-dimensional parallelisms of \({{\rm PG}(3, \mathbb{R})}\) of group dimension 1. 相似文献
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Eckehard W. Mielke 《Advances in Applied Clifford Algebras》2012,22(3):803-817
A topological field theory of gravity in four-dimension is proposed which is finite after quantization. Since such ‘minimal’ BF type models for the high energy limit are physically not quite realistic, a tiny symmetry breaking is needed to recover standard Einsteinian gravity for the macroscopic metrical background. 相似文献
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Vanderson Lima 《Annals of Global Analysis and Geometry》2017,51(2):189-208
Unlike \(\mathbb {R}^{3}\), the homogeneous spaces \(\mathbb {E}(-1,\tau )\) have a great variety of entire vertical minimal graphs. In this paper we explore conditions which guarantee that a minimal surface in \(\mathbb {E}(-1,\tau )\) is such a graph. More specifically, we introduce the definition of a generalized slab in \(\mathbb {E}(-1,\tau )\) and prove that a properly immersed minimal surface of finite topology inside such a slab region has multi-graph ends. Moreover, when the surface is embedded, the ends are graphs. When the surface is embedded and simply connected, it is an entire graph. 相似文献
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Doklady Mathematics - An autonomous object moves at a constant speed along the shortest path, while bypassing an ordered collection of pairwise disjoint convex sets. The object is tracked by an... 相似文献
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Yuichi Kabaya 《Geometriae Dedicata》2014,170(1):9-62
For an oriented surface of genus $g$ with $b$ boundary components, we construct a rational map from a subset of $\mathbb{C }^{6g-6+3b}$ onto an open algebraic subset of the $\text{ PSL }(2,\mathbb C )$ -character variety as an analogue of the Fenchel-Nielsen coordinates. After taking the quotient by an action of a finite group, we obtain a parametrization of a subset of the $\text{ PSL }(2,\mathbb C )$ -character variety, and similarly for the $\text{ SL }(2,\mathbb C )$ -character variety. We can systematically calculate a set of matrix generators by rational functions of the parameters. We give transformation formulae under elementary moves of pants decompositions. 相似文献
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Joaquim Borges Cristina Fernández-Córdoba Roger Ten-Valls 《Designs, Codes and Cryptography》2018,86(3):463-479
A binary linear code C is a \({\mathbb {Z}}_2\)-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the \({\mathbb {Z}}_2[x]\)-module \({\mathbb {Z}}_2[x]/(x^r-1)\times {\mathbb {Z}}_2[x]/(x^s-1).\) We determine the structure of \({\mathbb {Z}}_2\)-double cyclic codes giving the generator polynomials of these codes. We give the polynomial representation of \({\mathbb {Z}}_2\)-double cyclic codes and its duals, and the relations between the generator polynomials of these codes. Finally, we study the relations between \({{\mathbb {Z}}}_2\)-double cyclic and other families of cyclic codes, and show some examples of distance optimal \({\mathbb {Z}}_2\)-double cyclic codes. 相似文献
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Michelle Bucher-Karlsson 《Geometriae Dedicata》2007,125(1):203-224
We give the first complete proof of the strict positivity of the simplicial volume of compact locally symmetric spaces covered
by and show why the proof in [Savage RP, Trans Amer Math Soc 274(1):239–263, 1982] is incorrect.
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Georgios Dimitroglou Rizell Elizabeth Goodman Alexander Ivrii 《Geometric And Functional Analysis》2016,26(5):1297-1358
We show that, up to Lagrangian isotopy, there is a unique Lagrangian torus inside each of the following uniruled symplectic four-manifolds: the symplectic vector space \({{\mathbb{R}}^4}\), the projective plane \({{\mathbb{C}}P^2}\), and the monotone \({S^2 \times S^2}\). The result is proven by studying pseudoholomorphic foliations while performing the splitting construction from symplectic field theory along the Lagrangian torus. A number of other related results are also shown. Notably, the nearby Lagrangian conjecture is established for \({T^*{\mathbb{T}}^2}\), i.e. it is shown that every closed exact Lagrangian submanifold in this cotangent bundle is Hamiltonian isotopic to the zero-section. 相似文献
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Juncheol Pyo 《Annals of Global Analysis and Geometry》2011,40(2):167-176
We construct three kinds of complete embedded minimal surfaces in \({\mathbb {H}^2\times \mathbb {R}}\) . The first is a simply connected, singly periodic, infinite total curvature surface. The second is an annular finite total curvature surface. These two are conjugate surfaces just as the helicoid and the catenoid are in \({\mathbb {R}^3}\) . The third one is a finite total curvature surface which is conformal to \({\mathbb {S}^2\setminus\{p_1,\ldots,p_k\}, k\geq3.}\) 相似文献
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Biswas Indranil Schaposnik Laura P. Yang Mengxue 《Annals of Global Analysis and Geometry》2021,60(3):539-557
Annals of Global Analysis and Geometry - Since their introduction by Beilinson–Drinfeld (Opers, 1993. arXiv math/0501398; Quantization of Hitchin’s integrable system and Hecke... 相似文献