1. CJM Online first
 Cohen, David Bruce

Lipschitz 1connectedness for some solvable Lie groups
A space X is said to be Lipschitz 1connected if every LLipschitz loop in X bounds a O(L)Lipschitz disk. A Lipschitz 1connected space admits a quadratic isoperimetric inequality, but it is unknown whether the converse is true. Cornulier and Tessera showed that certain solvable Lie groups have quadratic isoperimetric inequalities, and we extend their result to show that these groups are Lipschitz 1connected.
Keywords:Dehn function, solvable group, lipschitz $1$connectedness Categories:20F65, 22E25 

2. CJM 2010 (vol 62 pp. 1116)
 Jin, Yongyang; Zhang, Genkai

Degenerate pLaplacian Operators and Hardy Type Inequalities on
HType Groups
Let $\mathbb G$ be a steptwo nilpotent group of Htype with Lie algebra $\mathfrak G=V\oplus \mathfrak t$. We define a class of vector fields $X=\{X_j\}$ on $\mathbb G$ depending on a real parameter $k\ge 1$, and we consider the corresponding $p$Laplacian operator $L_{p,k} u= \operatorname{div}_X (\nabla_{X} u^{p2} \nabla_X u)$. For $k=1$ the vector fields $X=\{X_j\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$; for $\mathbb G$ being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.
Keywords:fundamental solutions, degenerate Laplacians, Hardy inequality, Htype groups Categories:35H30, 26D10, 22E25 

3. CJM 2007 (vol 59 pp. 1301)
 Furioli, Giulia; Melzi, Camillo; Veneruso, Alessandro

Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group
We prove dispersive and Strichartz inequalities for the solution of the wave
equation related to the full
Laplacian on the Heisenberg group, by means of Besov spaces defined by a
LittlewoodPaley
decomposition related to the spectral resolution of the full Laplacian.
This requires a careful
analysis due also to the nonhomogeneous nature of the full Laplacian.
This result has to be compared to a previous one by Bahouri, G\'erard
and Xu concerning the solution of the wave equation related to
the Kohn Laplacian.
Keywords:nilpotent and solvable Lie groups, smoothness and regularity of solutions of PDEs Categories:22E25, 35B65 

4. CJM 2004 (vol 56 pp. 963)