On the Total Curvature of Bounded Portions of Surfaces

Intersection of minimal surfaces of boun

Intersection of minimal surfaces of bounded curvature

✍ Harold Rosenberg 📂 Article 📅 2001 🏛 Elsevier Science 🌐 French ⚖ 66 KB

Stably Embedded Surfaces of Bounded Inte

Stably Embedded Surfaces of Bounded Integral Curvature

✍ Joseph H.G. Fu 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 549 KB

We study the effect of simultaneous bounds on the local L 1 norms of the second fundamental form and of the Gauss curvature on the geometry of surfaces 7 embedded in a Riemannian manifold M. Such bounds are natural since (together with an area bound) they amount to a local bound on the area of the m

On bounds for total absolute curvature o

On bounds for total absolute curvature of surfaces in hyperbolic 3-space

✍ Rémi Langevin; Gil Solanes 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 98 KB

We construct examples of surfaces in hyperbolic space which do not satisfy the Chern-Lashof inequality (which holds for immersed surfaces in Euclidean space).

The geometry of total curvature on compl

The geometry of total curvature on complete open surfaces

✍ Katsuhiro Shiohama, Takashi Shioya, Minoru Tanaka 📂 Library 📅 2003 🏛 Cambridge University Press 🌐 English ⚖ 1 MB

This independent account of modern ideas in differential geometry shows how they can be used to understand and extend classical results in integral geometry. The authors explore the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, although their w

The geometry of total curvature on compl

The geometry of total curvature on complete open surfaces

✍ Shioya T., Shiohama K. 📂 Library 📅 2003 🏛 Cambridge University Press 🌐 English ⚖ 2 MB

This independent account of modern ideas in differential geometry shows how they can be used to understand and extend classical results in integral geometry. The authors explore the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, although their w

C1-smooth surfaces of bounded exterior p

C1-smooth surfaces of bounded exterior positive curvature

✍ S. Z. Shefel' 📂 Article 📅 1976 🏛 SP MAIK Nauka/Interperiodica 🌐 English ⚖ 145 KB