4 citations · 4 across the 7 of their papers we have counts for
7 papers
Density of a minimal submanifold and total curvature of its boundary
Jaigyoung Choe, Robert Gulliver
Given a piecewise smooth submanifold and , we define the {\em vision angle} to be the -dimensional volume of the radial projectio…
Branch points of area-minimizing projective planes
Robert Gulliver
Minimal surfaces in a Riemannian manifold are surfaces which are stationary for area: the first variation of area vanishes. In this paper we focus on surfaces of the topologi…
Total Curvature of Graphs after Milnor and Euler
Robert Gulliver, Sumio Yamada
We define a new notion of total curvature, called net total curvature, for finite graphs embedded in Rn, and investigate its properties. Two guiding principles are given by Milnor'…
Regularity of soap film-like surfaces spanning graphs in a Riemannian manifold
Robert Gulliver, Sung-ho Park, Juncheol Pyo +1
Let be an -dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant . Using the cone total curvature…
Examples of hypersurfaces flowing by curvature in a Riemannian manifold
Robert Gulliver, Guoyi Xu
This paper gives some examples of hypersurfaces evolving in time with speed determined by functions of the normal curvatures in an -dimensional hyperbolic manifol…
Total curvature and isotopy of graphs in
Robert Gulliver, Sumio Yamada
Knot theory is the study of isotopy classes of embeddings of the circle into a 3-manifold, specifically . The Fáry-Milnor Theorem says that any curve in of total c…
Area density and regularity for soap film-like surfaces spanning graphs
Robert Gulliver, Sumio Yamada
For a given boundary set consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area density of a soap film-like surf…