论文标题
sobolev-gaffney类型的不平等现象的差分形式的不平等现象，划分的几何形状
Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry
论文作者
论文摘要
在本文中，我们建立了$ w^{\ ell，p} $ - sobolev空间的gaffney类型不等式，用于次级利曼式接触歧管上没有边界的差分形式，具有有界的几何形状（因此，尤其是，我们在脑海中脑海中有非紧密歧管）。在这里，$ p \ in] 1，\ infty [$ and $ \ ell = 1,2 $，具体取决于我们正在考虑的差分表格的顺序。证明取决于Baldi-Franchi在Heisenberg组的环境中证明的Sobolev-Gaffney不平等中的Rumin差异形式的结构，并在Heisenberg群体的情况下证明了一些几何特性，以及一些几何特性，这些几何特性可以证明具有限定的几何形式的次利曼式接触歧管。
In this paper we establish a Gaffney type inequality, in $W^{\ell,p}$-Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded geometry (hence, in particular, we have in mind non-compact manifolds). Here $p\in]1,\infty[$ and $\ell=1,2$ depending on the order of the differential form we are considering. The proof relies on the structure of the Rumin's complex of differential forms in contact manifolds, on a Sobolev-Gaffney inequality proved by Baldi-Franchi in the setting of the Heisenberg groups and on some geometric properties that can be proved for sub-Riemannian contact manifolds with bounded geometry.
