an:06241374
Zbl 1282.26016
Trudinger, Neil S.; Zhang, Wei
Hessian measures on the Heisenberg group
EN
J. Funct. Anal. 264, No. 10, 2335-2355 (2013).
00327803
2013
j
26B25 28A33 35J60 35R03
Hessian measures; Heisenberg group; monotonicity formula
In the context of the Heisenberg group, several notions of convexity have been presented by various researchers. Several authors, simultaneously, presented the notion of convexity, e.g. \textit{N. S. Trudinger} and \textit{X.-J.Wang} [Topol. Methods Nonlinear Anal. 10, No. 2, 225--239 (1997; Zbl 0915.35039)]. In the present paper, the authors study the properties of \(k\)-convex functions on the Heisenberg group and prove the weak continuity of the \(k\)-Hessian measure in the Euclidean space corresponding to the case that appears in [loc. cit.]. Resolving the Garofalo-Tournier conjecture, the monotonicity formula is proved in Section 3 for cases \(n>2\).
Deshna Loonker (Jodhpur)
Zbl 0915.35039