论文标题
riemannian表面的对称和等法
Symmetry and Isoperimetry for Riemannian Surfaces
论文作者
论文摘要
对于域的$ω$，在地球上凸面中，我们引入了散射能量$ \ MATHCAL {E}（ω）$，该$通过量化其与等距圆动作的不兼容来测量$ω$的不对称性。我们证明了涉及$ \ Mathcal {e}（ω）$的几个尖锐的定量等级不等式，并通过散射能量通过凸和旋转对称性来表征域而来的域。我们还为Riemannian表面尖锐的Sobolev不等式提供了新的证明，该表面独立于等等不平等。
For a domain $Ω$ in a geodesically convex surface, we introduce a scattering energy $\mathcal{E}(Ω)$, which measures the asymmetry of $Ω$ by quantifying its incompatibility with an isometric circle action. We prove several sharp quantitative isoperimetric inequalities involving $\mathcal{E}(Ω)$ and characterize the domains with vanishing scattering energy by their convexity and rotational symmetry. We also give a new proof of the sharp Sobolev inequality for Riemannian surfaces which is independent of the isoperimetric inequality.
