All Questions
3 questions
6
votes
1
answer
3k
views
Difference between the Laplacian and the sub-Laplacian of a Lie group
Given a Lie group $G$, what is the difference between the Laplacian $\Delta$ and the sub-Laplacian $\Delta_{sub}$ of $G$. And what are the properties that we lose when going from sub-Laplace to ...
- 650
4
votes
1
answer
413
views
Heisenberg groups, Carnot groups and contact forms
The horizontal distribution in the Heisenberg group is the kernel of the standard contact form:
$$
\alpha = dt + 2 \sum_{j=1}^n (x_j \, dy_j - y_j \, dx_j).
$$
Question. Can one describe ...
- 28k
4
votes
1
answer
234
views
dirichlet problem in the heisenberg group
Good morning everybody.
I was looking just for a quick reference to know whether the Dirichlet problem has a solution in the Heisenberg group, that is $\mathbb R^3$ endowed with coordinates $(x,y,z)$ ...
- 277