Regularity of convex functions on Heisenberg groups

Zoltán M. Balogh; Matthieu Rickly

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)

  • Volume: 2, Issue: 4, page 847-868
  • ISSN: 0391-173X

Abstract

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We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-convexity) are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines.

How to cite

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Balogh, Zoltán M., and Rickly, Matthieu. "Regularity of convex functions on Heisenberg groups." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.4 (2003): 847-868. <http://eudml.org/doc/84522>.

@article{Balogh2003,
abstract = {We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-convexity) are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines.},
author = {Balogh, Zoltán M., Rickly, Matthieu},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {847-868},
publisher = {Scuola normale superiore},
title = {Regularity of convex functions on Heisenberg groups},
url = {http://eudml.org/doc/84522},
volume = {2},
year = {2003},
}

TY - JOUR
AU - Balogh, Zoltán M.
AU - Rickly, Matthieu
TI - Regularity of convex functions on Heisenberg groups
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2003
PB - Scuola normale superiore
VL - 2
IS - 4
SP - 847
EP - 868
AB - We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-convexity) are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines.
LA - eng
UR - http://eudml.org/doc/84522
ER -

References

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