Abstract
We prove that h-convex functions on Carnot groups of step two are locally Lipschitz continuous with respect to any intrinsic metric. We show that an additional measurability condition implies the local Lipschitz continuity of h-convex functions on arbitrary Carnot groups.
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Communicated by Peter Li
To the Memory of Q. G.
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Rickly, M. First-order regularity of convex functions on Carnot Groups. J Geom Anal 16, 679–702 (2006). https://doi.org/10.1007/BF02922136
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DOI: https://doi.org/10.1007/BF02922136