minkowski planes
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2021 ◽  
Vol 18 (2) ◽  
pp. 279-284
Author(s):  
Vladimir Zorich

We discuss several topics: the concept of conformal mapping of Riemannian and pseudo-Riemannian manifolds, conformal rigidity of higher-dimensional domains, and conformal flexibility of two-dimensional domains of Euclidian and Minkowski planes. We present an extension of the concept of conformal mapping proposed by M. Gromov and recall an open problem related to it.


2020 ◽  
Vol 20 (4) ◽  
pp. 585-594
Author(s):  
Brendan Creutz ◽  
Duy Ho ◽  
Günter F. Steinke

AbstractWe contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to PSL(2, ℝ). Using this result, we describe a framework for the full classification based on the action of the group on the point set.


2020 ◽  
Vol 94 (5) ◽  
pp. 969-977
Author(s):  
Márton Naszódi ◽  
Vilmos Prokaj ◽  
Konrad Swanepoel

2020 ◽  
Vol 0085 ◽  
pp. 21-30
Author(s):  
Mostafa Ghandehari ◽  
Horst Martini

2018 ◽  
Vol 55 (2) ◽  
pp. 174-189
Author(s):  
Mostafa Ghandehari ◽  
Horst Martini

In the Euclidean plane, the Erdős-Mordell inequality indicates that the sum of distances of an interior point of a triangle T to its vertices is larger than or equal to twice the sum of distances to the sides of T. We extend this theorem to arbitrary (normed or) Minkowski planes, and we generalize in an analogous way some other related inequalities, e.g. referring to polygons. We also derive Minkowskian analogues of Erdős-Mordell inequalities for tetrahedra and n-dimensional simplices. Finally, some related inequalities are obtained which additionally involve total edge-lengths of simplices.


2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Günter F. Steinke

AbstractWe construct anew family of flat Minkowski planes that admit the simple group PSL


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