Christoffel–Minkowski problem

E947537

mathematical problem problem in convex geometry

The Christoffel–Minkowski problem is a classical question in convex geometry that seeks to reconstruct a convex body from prescribed curvature or area measure data on the unit sphere.

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All labels observed (3)

Label	Occurrences
Minkowski problem	2
Aleksandrov problem	1
Christoffel–Minkowski problem canonical	1

Statements (44)

Predicate	Object
instanceOf	mathematical problem ⓘ problem in convex geometry ⓘ
appearsIn	modern convex geometric analysis literature ⓘ
appliesTo	convex bodies in Euclidean space ⓘ convex hypersurfaces ⓘ
asksFor	reconstruction of a convex body from area measure ⓘ reconstruction of a convex body from curvature data ⓘ
concerns	area measures on the sphere ⓘ convex bodies ⓘ curvature measures ⓘ
connectedTo	Aleksandrov–Fenchel inequalities NERFINISHED ⓘ isoperimetric-type inequalities ⓘ
dimension	n-dimensional Euclidean space ⓘ
domain	unit sphere ⓘ
field	convex geometry ⓘ geometric analysis ⓘ partial differential equations ⓘ
generalizationOf	classical Minkowski problem ⓘ
goal	characterize which measures on the sphere arise from convex bodies ⓘ
hasAspect	existence of convex bodies with given curvature measure ⓘ regularity of solutions ⓘ uniqueness of convex bodies with given curvature measure ⓘ
hasCondition	balance conditions on the prescribed measure ⓘ positivity conditions on the prescribed measure ⓘ
involves	Gauss curvature ⓘ measure on the unit sphere ⓘ prescribed curvature on the unit sphere ⓘ support function of a convex body ⓘ surface area measure ⓘ
namedAfter	Elwin Bruno Christoffel NERFINISHED ⓘ Hermann Minkowski NERFINISHED ⓘ
relatedTo	Aleksandrov problem NERFINISHED ⓘ Brunn–Minkowski theory NERFINISHED ⓘ Christoffel problem NERFINISHED ⓘ Minkowski problem NERFINISHED ⓘ Monge–Ampère equation NERFINISHED ⓘ
status	partially solved in various dimensions and regularity classes ⓘ
studiedIn	differential geometry ⓘ measure theory ⓘ
typeOf	geometric reconstruction problem ⓘ inverse problem ⓘ
uses	curvature integrals ⓘ nonlinear elliptic PDEs ⓘ spherical measures ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Elwin Bruno Christoffel → notableWork → Christoffel–Minkowski problem ⓘ

Monge–Ampère equation → usedIn → Christoffel–Minkowski problem ⓘ

this entity surface form: Minkowski problem

Monge–Ampère equation → usedIn → Christoffel–Minkowski problem ⓘ

this entity surface form: Aleksandrov problem

Shing-Tung Yau → knownFor → Christoffel–Minkowski problem ⓘ

this entity surface form: Minkowski problem