DOAJ Open Access 2014

Polytopes and $C^1$-convex bodies

Karim Adiprasito José Alejandro Samper

Lihat Sumber DOI

Abstrak

The face numbers of simplicial polytopes that approximate $C^1$-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence $\{P_n\}_{n=0}^{\infty}$ of simplicial polytopes converges to a $C^1$-convex body in the Hausdorff distance, then the entries of the $g$-vector of $P_n$ converge to infinity.

Topik & Kata Kunci

Mathematics

Penulis (2)

Karim Adiprasito

José Alejandro Samper

Format Sitasi

APA MLA BibTeX

Adiprasito, K., Samper, J.A. (2014). Polytopes and $C^1$-convex bodies. https://doi.org/10.46298/dmtcs.2399

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2399

Informasi Jurnal

Tahun Terbit: 2014
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2399
Akses: Open Access ✓