Volume, surface area and inward injectivity radius
Nobuhiro Innami · Proceedings of the American Mathematical Society · 1999
We show some relations among the volumes of domains in Euclidean spaces, their surface areas and the inward injectivity radii from their boundaries. In particular, we give an estimate for the upper bound of the ratios of their surface areas and volumes by means of inward injectivity radii. The upper bound seems to depend on their topological structures.