An estimate from below for the spatial diameter of a surface in terms of its intrinsic radius and curvature
Abstract
In this paper we prove the following Theorem.Let$F$be a regular simply connected surface of class$C^3$in$R^3$. There exist postitive absolute constants$C$and$C_1$such that if$$ \mu=\int_F|K|\,dS<C, $$where$K$is the Gaussian curvature and$S$is the area element on$F$, the estimate$$ d\geqslant\bigl(\sqrt3-C_1\sqrt\mu\bigr)r $$holds.Bibliography: 11 titles.
Submission history
[v1] 1971