Hessian measures on the Heisenberg group

详细信息    查看全文

• 作者：Neil S. Trudinger ; ^{neil.trudinger@anu.edu.au} ; Wei Zhang ^{wei.zhang@anu.edu.au}
• 关键词：Hessian measures ; Heisenberg group ; Weak convergence ; Monotonicity formula
• 刊名：Journal of Functional Analysis
• 出版年：2013
• 出版时间：15 May, 2013
• 年：2013
• 卷：264
• 期：10
• 页码：2335-2355
• 全文大小：208 K

文摘

In this paper, we study the properties of k-convex functions on the Heisenberg group , for and prove the weak continuity of k-Hessian measures with respect to local uniform convergence in the Heisenberg setting. Our approach through monotonicity formulae makes use of previous research in the corresponding Euclidean case of Trudinger and Wang. The case provides an analogue of the Monge-Amp¨¨re measure of Aleksandrov for . We also answer a conjecture of Garofalo and Tournier on monotonicity for the cases .