论文标题
关于Riemannian模型的一些强烈的庞加莱不平等现象及其改进
On some strong Poincaré inequalities on Riemannian models and their improvements
论文作者
论文摘要
我们证明，第二和第四阶改善了涉及强硬型剩余条款的双曲线空间上的庞加莱型不平等现象。因为他们的L.H.S.仅涉及梯度的径向部分或laplacian的径向部分，它们可以看作是经典庞加莱不平等的更强版本。我们表明，在适当的曲率假设和某些常数的清晰度下，这种不平等也是在模型歧管上的正确性。
We prove second and fourth order improved Poincaré type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as stronger versions of the classical Poincaré inequality. We show that such inequalities hold true on model manifolds as well, under suitable curvature assumptions and sharpness of some constants is also discussed.
