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...

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...

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...

radial isometry, and is of fundamental importance in the study of geodesic convexity and normal coordinates. We define the exponential map at p ∈ M {\displaystyle...

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

that every compact set has a compact convex hull, as defined using geodesic convexity. The curve-shortening flow cannot cause a curve to depart from its...

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)...