Convex polytopes, dihedral angles, mean curvature and scalar curvature (Q6624181)

From MaRDI portal





scientific article; zbMATH DE number 7931803
Language Label Description Also known as
English
Convex polytopes, dihedral angles, mean curvature and scalar curvature
scientific article; zbMATH DE number 7931803

    Statements

    Convex polytopes, dihedral angles, mean curvature and scalar curvature (English)
    0 references
    0 references
    25 October 2024
    0 references
    This deep and interesting paper derives lower bounds on the dihedral angles of polytopes in \(\mathbb{R}^d\) by applying techniques from differential geometry to smooth approximating bodies, and constructs some interesting examples of polytopes with nontrivial upper bounds on their dihedral angles.\N\NThe reader is warned that the notation is sometimes nonconventional (\textit{e.g.}, bullet points with subscripts) and challenging to follow (both the regular hexagon and the regular octagon appear as symbols, at a point size that makes them hard to distinguish.) The word ``complement[ary]'' is used where ``supplement[ary]'' would be customary.
    0 references
    0 references
    geometric measure theory
    0 references
    approximation theorems
    0 references
    polytopes
    0 references
    Riemannian manifolds
    0 references

    Identifiers

    0 references
    0 references
    0 references
    0 references
    0 references