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Search: All articles in the CMB digital archive with keyword plane

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1. CMB 2014 (vol 57 pp. 697)

Bailet, Pauline
 On the Monodromy of Milnor Fibers of Hyperplane Arrangements We describe a general setting where the monodromy action on the first cohomology group of the Milnor fiber of a hyperplane arrangement is the identity. Keywords:hyperplane arrangements, Milnor fiber, monodromy, local systemsCategories:32S22, 32S55, 32S25, 32S40

2. CMB 2013 (vol 57 pp. 72)

Grari, A.

3. CMB 2013 (vol 57 pp. 821)

Jeong, Imsoon; Kim, Seonhui; Suh, Young Jin
 Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator In this paper we give a characterization of a real hypersurface of Type~$(A)$ in complex two-plane Grassmannians ${ { {G_2({\mathbb C}^{m+2})} } }$, which means a tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in ${G_2({\mathbb C}^{m+2})}$, by the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$. Keywords:real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operatorCategories:53C40, 53C15

4. CMB 2011 (vol 56 pp. 593)

Liu, Congwen; Zhou, Lifang
 On the $p$-norm of an Integral Operator in the Half Plane We give a partial answer to a conjecture of DostaniÄ on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane. Keywords:Bergman projection, integral operator, $L^p$-norm, the upper half planeCategories:47B38, 47G10, 32A36

5. CMB 2011 (vol 55 pp. 767)

Martini, Horst; Wu, Senlin
 On Zindler Curves in Normed Planes We extend the notion of Zindler curve from the Euclidean plane to normed planes. A characterization of Zindler curves for general normed planes is given, and the relation between Zindler curves and curves of constant area-halving distances in such planes is discussed. Keywords:rc length, area-halving distance, Birkhoff orthogonality, convex curve, halving pair, halving distance, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curveCategories:52A21, 52A10, 46C15

6. CMB 2010 (vol 53 pp. 629)

Chinen, Naotsugu; Hosaka, Tetsuya
 Asymptotic Dimension of Proper CAT(0) Spaces that are Homeomorphic to the Plane In this paper, we investigate a proper CAT(0) space $(X,d)$ that is homeomorphic to $\mathbb R^2$ and we show that the asymptotic dimension $\operatorname{asdim} (X,d)$ is equal to $2$. Keywords:asymptotic dimension, CAT(0) space, planeCategories:20F69, 54F45, 20F65

7. CMB 2009 (vol 52 pp. 424)

Martini, Horst; Spirova, Margarita
 Covering Discs in Minkowski Planes We investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by $k$ unit circles. In particular, we study the cases $k=3$, $k=4$, and $k=7$. For $k=3$ and $k=4$, the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, $d$-segments, and the monotonicity lemma. Keywords:affine regular polygon, bisector, circle covering problem, circumradius, $d$-segment, Minkowski plane, (strictly convex) normed planeCategories:46B20, 52A21, 52C15

8. CMB 2005 (vol 48 pp. 523)

Düvelmeyer, Nico
 Angle Measures and Bisectors in Minkowski Planes \begin{abstract} We prove that a Minkowski plane is Euclidean if and only if Busemann's or Glogovskij's definitions of angular bisectors coincide with a bisector defined by an angular measure in the sense of Brass. In addition, bisectors defined by the area measure coincide with bisectors defined by the circumference (arc length) measure if and only if the unit circle is an equiframed curve. Keywords:Radon curves, Minkowski geometry, Minkowski planes,, angular bisector, angular measure, equiframed curvesCategories:52A10, 52A21