论文标题
在低$ n $加权的RICCI曲率界限下与$ \ varepsilon $ -range下的歧管的比较几何形状与边界的比较几何形状
Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $\varepsilon$-range
论文作者
论文摘要
我们研究了在$ n $ n $ n $ n $ n $ n $ n $ n \ in] - \ infty，1] \ cup [n，+\ infty] $的较低$ n $ n $加权曲率下的比较几何形状。我们将得出结论，并比较刻有半径的半径，边界周围的体积以及加权$ p $ -laplacian的最小的dirichlet特征值的几何结果。我们的结果将这些结果插入[n，+\ infty [$ and $ \ varepsilon = 1 $，以及$ n \ in] - \ infty，1] $和$ \ varepsilon = 0 $的$ n \ in [n，+\ \ \ varepsilon = 1 $中的插入。
We study comparison geometry of manifolds with boundary under a lower $N$-weighted Ricci curvature bound for $N\in ]-\infty,1]\cup [n,+\infty]$ with $\varepsilon$-range introduced by Lu-Minguzzi-Ohta. We will conclude splitting theorems, and also comparison geometric results for inscribed radius, volume around the boundary, and smallest Dirichlet eigenvalue of the weighted $p$-Laplacian. Our results interpolate those for $N\in [n,+\infty[$ and $\varepsilon=1$, and for $N\in ]-\infty,1]$ and $\varepsilon=0$ by the second named author.
