# On Green functions for Dirichlet sub-Laplacians on H-type groups

## TL;DR

This paper constructs explicit Green functions for Dirichlet problems of sub-Laplacians on unbounded domains in H-type groups, providing solutions for various boundary conditions and geometries.

## Contribution

It introduces explicit Green functions for sub-Laplacians on H-type groups and solves Dirichlet problems in several unbounded domains with non-zero boundary data.

## Key findings

- Explicit Green functions for Dirichlet problems on H-type groups
- Solutions for boundary value problems in half-space, quadrant, and strip domains
- Methodology applicable to unbounded domains in sub-Riemannian geometry

## Abstract

We construct Green functions of Dirichlet boundary value problems for sub-Laplacians on certain unbounded domains of a prototype Heisenberg-type group (prototype H-type group, in short). We also present solutions in an explicit form of the Dirichlet problem for the sub-Laplacian with non-zero boundary datum on half-space, quadrant-space, etc, as well as in a strip.