Geodesic convexity information

geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix "geodesic"...

namely any two points in it are joined by a unique geodesic. This property is called "geodesic convexity" and the coordinates are called "normal coordinates"...

Convex analysis Convex conjugate Convex curve Convex optimization Geodesic convexity Hahn–Banach theorem Hermite–Hadamard inequality Invex function Jensen's...

infimum of length (a geodesic) then it is called a geodesic metric space or geodesic space. For instance, the Euclidean plane is a geodesic space, with line...

Euclidean by defining a geodesically convex set to be one that contains the geodesics joining any two points in the set. Convexity can be extended for a...

of convexity at a point p of a Riemannian manifold is the largest radius of a ball which is a convex subset. Ray is a one side infinite geodesic which...

path-connectedness (see the example of the rational numbers) nor does it imply geodesic convexity for Riemannian manifolds (consider, for example, the Euclidean plane...

f(tx + (1 − t)y) ≤ max(f(x), f(y)) for t ∈ [0,1] Subderivative Geodesic convexity — convexity for functions defined on a Riemannian manifold Duality (optimization)...

reparametrized to be geodesics, and any geodesic must satisfy the Euler–Lagrange equation for E[γ]. Assuming the strong convexity of F2 there exists a...

Haefliger 1999, pp. 271–272 In geodesic normal coordinates, the metric g(x) = I + ε ‖ x ‖. By geodesic convexity, a geodesic from p to q lies in the ball...

the number of sides. Polygons may be characterized by their convexity or type of non-convexity: Convex: any line drawn through the polygon (and not tangent...

geometrical continuous-space concepts such as size, shape, convexity, connectivity, and geodesic distance, were introduced by MM on both continuous and discrete...

discrete geometry and computational geometry, the relative convex hull or geodesic convex hull is an analogue of the convex hull for the points inside a simple...

becomes a geodesic: a curve which is a distance-preserving function. A geodesic is a shortest possible path between any two of its points. A geodesic metric...

shapes, and are called critical support lines. Without the assumption of convexity, there may be more or fewer than four lines of support, even if the shapes...

non-positive curvature, Springer Papadopoulos, Athanase (2014), Metric spaces, convexity and non-positive curvature, IRMA Lectures in Mathematics and Theoretical...

totally geodesic compact submanifolds must intersect if their dimensions are large enough. The idea is to apply Synge's method to a minimizing geodesic between...

combinatorics. In economics, convex hulls can be used to apply methods of convexity in economics to non-convex markets. In geometric modeling, the convex...

several proofs of this, some of the more recent ones related to results in convexity theory, the geometry of numbers and circle packing, such as the Brunn–Minkowski...

group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric space. This notion generalizes the notions of a hyperbolic...