3 citations · 3 across the 4 of their papers we have counts for
5 papers
Warped products admitting a curvature bound
Stephanie B. Alexander, Richard L. Bishop
This paper completes a fundamental construction in Alexandrov geometry. Previously we gave a new construction of metric spaces with curvature bounds either above or below, namely w…
Riemannian Geometry
Richard L. Bishop
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the backg…
Total curvature and simple pursuit on domains of curvature bounded above
S. Alexander, R. Bishop, R. Ghrist
We show how circumradius and asymptotic behavior of curves in CAT(0) and CAT(K) spaces(K>0) are controlled by growth rates of total curvature. We apply our results to pursuit and e…
The intrinsic geometry of a Jordan domain
Richard L. Bishop
For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a CAT(0)space and Gromov hyperbolic. With respect t…
Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above
Stephanie B. Alexander, Richard L. Bishop
A Gauss equation is proved for subspaces of Alexandrov spaces of curvature bounded above by K. That is, a subspace of extrinsic curvature less than or equal to A, defined by a cubi…