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Algorithms and Combinatorics, 1997 Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc.
Monique Laurent, Michel Marie Deza
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Cayley–Klein Geometries and Projective-Metric Geometry
Journal of Geometry, 2022There is something profoundly unsatisfactory with the traditional algebraic definition of plane Cayley-Klein geometries, and this important paper ingeniously remedies those shortcomings for the first time. Following Felix Klein, the standard introduction of analytically described Cayley-Klein geometries proceeeds over the field of real numbers by the ...
Rolf Struve, Horst Struve
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Metric Geometry of the Kobayashi Metric
European Journal of Mathematics, 2017This is a survey article presenting some results related to the Kobayashi metric for domains in \(\mathbb C^n\). Among others, the authors discuss estimates of the Kobayashi metric near the boundary, extensions of the biholomorphic mappings to boundaries, convexity and complex geodesics, isometries of the Kobayashi metric, and Gromov hyperbolicity.
Harish Seshadri, Hervé Gaussier
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Metric-Affine Geometries With Spherical Symmetry [PDF]
Symmetry, 2020 We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss the most general class of such geometries, which we display both in the metric-Palatini formulation and in the ...
Manuel Höhmann
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2020
In this chapter we shall consider some geometric issues related to the hyperbolic or quasihyperbolic metric. We begin with several comparison results for the quasihyperbolic metric. Here an important fact is that various metrics may be comparable in some but not in all domains.
Parisa Hariri +2 more
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In this chapter we shall consider some geometric issues related to the hyperbolic or quasihyperbolic metric. We begin with several comparison results for the quasihyperbolic metric. Here an important fact is that various metrics may be comparable in some but not in all domains.
Parisa Hariri +2 more
openaire +1 more source
Metric bases in digital geometry
Computer Vision, Graphics, and Image Processing, 1984The authors consider the set D of all points in the Euclidean plane with integral coordinates (digital plane). Given a metric d on \(A\subset D\), a subset \(S\subset A\) is called a metric basis for A if \(d(x,s)=d(y,s)\) for all \(s\in S\) implies \(x=y.\) It is well known that a minimal metric basis for the Euclidean plane with respect to the ...
Robert A. Melter, Ioan Tomescu
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Convergence in Metric Differential Geometry
Communications of the Korean Mathematical Society, 2003 Summary: We use geometric properties of Gromov-Hausdorff-con-vergence to present a way to construct rough but natural invariants of metric geometry.
Kim, Young Wook, Lee, Hyoung Yong
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