Comparison theory of distance spheres along geodesics
In this interesting paper the author proves several new bounds on the Hessian and the Laplacian of the distance function from a point along a geodesic in a complete Riemannian manifold under the assumption of lower bounds on sectional or Ricci curvature and on the conjugate or focal radius. The new bounds give information about the second fundamental form and mean curvature of the geodesic spheres about the point.
scientific article; zbMATH DE number 7291222
scientific article