TY - JOUR

T1 - Uniqueness theorem for locally antipodal Delaunay sets

AU - Dolbilin, N. P.

AU - Magazinov, A. N.

N1 - Publisher Copyright:
© 2016, Pleiades Publishing, Ltd.

PY - 2016/8/1

Y1 - 2016/8/1

N2 - We prove theorems on locally antipodal Delaunay sets. The main result is the proof of a uniqueness theorem for locally antipodal Delaunay sets with a given 2R-cluster. This theorem implies, in particular, a new proof of a theorem stating that a locally antipodal Delaunay set all of whose 2R-clusters are equivalent is a regular system, i.e., a Delaunay set on which a crystallographic group acts transitively.

AB - We prove theorems on locally antipodal Delaunay sets. The main result is the proof of a uniqueness theorem for locally antipodal Delaunay sets with a given 2R-cluster. This theorem implies, in particular, a new proof of a theorem stating that a locally antipodal Delaunay set all of whose 2R-clusters are equivalent is a regular system, i.e., a Delaunay set on which a crystallographic group acts transitively.

UR - http://www.scopus.com/inward/record.url?scp=84992065919&partnerID=8YFLogxK

U2 - 10.1134/S0081543816060134

DO - 10.1134/S0081543816060134

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AN - SCOPUS:84992065919

SN - 0081-5438

VL - 294

SP - 215

EP - 221

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

IS - 1

ER -