ON REVERSE ISOPERIMETRIC INEQUALITIES IN TWO-DIMENSIONAL SPACE FORMS AND RELATED RESULTS

摘要

In this paper, we investigate the curvature radius of strictly convex domains in two-dimensional space forms. We obtain a class of new reverse isoperimetric inequalities which provide a measure for the deviation of a strictly convex domain from a geodesic disc, via the maximum and the minimum of the curvature radius of its boundary.