论文信息 - Equilateral dimension of the Heisenberg group - 字舞流文

Equilateral dimension of the Heisenberg group

Let H be the first Heisenberg group equipped with the Korányi metric d. We prove that the equilateral dimension of H is 4.

J.Kim | I. D. Platis

[1] L. Danzer,et al. Über zwei Probleme bezüglich konvexer Körper von P. Erdös und von V. L. Klee , 1962 .

[2] K. Swanepoel. Equilateral sets in finite-dimensional normed spaces , 2004, math/0406264.

[3] Konrad J. Swanepoel. A problem of Kusner on equilateral sets , 2003 .

[4] Peter Braß. On equilateral simplices in normed spaces , 1997 .

[5] Jeremy A. Mann. Equilateral Dimension of Riemannian Manifolds with Bounded Curvature , 2013 .

[6] Ara Basmajian,et al. COMPLEX HYPERBOLIC GEOMETRY (Oxford Mathematical Monographs) , 2001 .

[7] C. Petty,et al. Equilateral sets in Minkowski spaces , 1971 .

[8] J. Tyson,et al. Marstrand's density theorem in the Heisenberg group , 2014, 1407.6636.