Comparison geometry of manifolds with boundary under lower N-weighted Ricci curvature bounds with e-range

摘要

We study comparison geometry of manifolds with boundary under a lower N-weighted Ricci curvature bound for N E] - oo, 1] U [n, +co] with e-range introduced by Lu-Minguzzi-Ohta in 2022. 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 E [n, +oo[ and e = 1, and for N E] - 00, 1] and e = 0 by the second named author.