Sharp measure contraction property for generalized H-type Carnot groups - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2017

Sharp measure contraction property for generalized H-type Carnot groups

Luca Rizzi

Résumé

We prove that H-type Carnot groups of rank k and dimension n satisfy the MCP(K, N) if and only if K ≤ 0 and N ≥ k + 3(n − k). The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. This constitutes the largest class of Carnot groups for which the curvature exponent coincides with the geodesic dimension. We stress that generalized H-type Carnot groups have step 2, include all corank 1 groups and, in general, admit abnormal minimizing curves. As a corollary, we prove the absolute continuity of the Wasserstein geodesics for the quadratic cost on all generalized H-type Carnot groups.
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Dates et versions

hal-01468967 , version 1 (16-02-2017)
hal-01468967 , version 2 (06-11-2017)

Identifiants

  • HAL Id : hal-01468967 , version 1

Citer

Davide Barilari, Luca Rizzi. Sharp measure contraction property for generalized H-type Carnot groups. 2017. ⟨hal-01468967v1⟩
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