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math.DG2024
Stretch maps on the affine-additive group
Z. M. Balogh, E. Bubani, I. D. Platis
We define linear and radial stretch maps in the affine-additive group, and prove that they are minimizers of the mean quasiconformal distortion functional. For the proofs we use a…
math.GT2024
Geodesics on the Kahler cone of the Heisenberg group
Joonhyung Kim, Ioannis D. Platis, Li-Jie Sun
In this paper we describe the geodesics on the Kähler cone of the Heisenberg group. Furthermore we also prove that this is not a complete manifold.
math.MG2024
Hyperbolicity of the sub-Riemannian affine-additive group
Zoltán M. Balogh, Elia Bubani, Ioannis D. Platis
We consider the affine-additive group as a metric measure space with a canonical left-invariant measure and a left-invariant sub-Riemannian metric. We prove that this metric measur…