A four vertex theorem for strictly convex space curves
نویسندگان
چکیده
منابع مشابه
A Four-vertex Theorem for Space Curves
We prove a vertex theorem for space curves which need not lie on the boundaries of their convex hulls.
متن کاملA Convex Decomposition Theorem for Four - Manifolds
In this article we show that every smooth closed oriented fourmanifold admits a decomposition into two submanifolds along common boundary. Each of these submanifolds is a complex manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-manifold is a Stein domain in the the complement of a certain contractible 2-complex.
متن کاملMorse-sard Theorem for Delta-convex Curves
Let Z and X be Banach spaces, U ⊂ Z an open convex set and f : U → X a mapping. We say that f is a delta-convex mapping (d. c. mapping) if there exists a continuous convex function h on U such that y ◦ f + h is a continuous convex function for each y ∈ Y , ‖y∗‖ = 1. We say that f : U → X is locally d. c. if for each x ∈ U there exists an open convex U ′ such that x ∈ U ′ ⊂ U and f |U ′ is d. c....
متن کاملA Proof of Sudakov Theorem with Strictly Convex Norms
We establish a solution to the Monge problem in N , with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor un...
متن کاملA Riemannian Four Vertex Theorem for Surfaces with Boundary
We prove that every metric of constant curvature on a compact surface M with boundary ∂M induces at least four vertices, i.e., local extrema of geodesic curvature, on a connected component of ∂M , if, and only if, M is simply connected. Indeed, when M is not simply connected, we construct hyperbolic, parabolic, and elliptic metrics of constant curvature on M with only two critical points of geo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry
سال: 1993
ISSN: 0047-2468,1420-8997
DOI: 10.1007/bf01231004