Cover Image

Non-continuous valuations on convex bodies and a new characterization of volume

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Marcos, Jorge S. Ibáñez, Tradacete, Pedro, Villanueva, Ignacio
Format:	Preprint
Published:	2025
Subjects:	Metric Geometry 52B45 (Primary) 52A40 (Secondary)
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations
by: Bernig, Andreas, et al.
Published: (2023)

Smooth valuations on convex bodies and finite linear combinations of mixed volumes
by: Knoerr, Jonas
Published: (2023)

On the minimal area of quadrangles circumscribed about planar convex bodies
by: Fodor, Ferenc, et al.
Published: (2025)

A strengthening of the Blaschke-Santaló inequality for $o$-symmetric planar convex bodies
by: Böröczky, Károly J., et al.
Published: (2026)

Valuations in affine convex geometry
by: Henkel, Jakob, et al.
Published: (2023)

Zonal valuations on convex bodies
by: Knoerr, Jonas
Published: (2024)

Strengthened inequalities for the mean width and the $\ell$-norm of origin symmetric convex bodies
by: Böröczky, Károly J., et al.
Published: (2024)

On Bezdek's conjecture for high-dimensional convex bodies with an aligned center of symmetry
by: Alfonseca, M. Angeles, et al.
Published: (2025)

On the illumination of 1-symmetric convex bodies
by: Sun, Wen Rui, et al.
Published: (2024)

Spherical coverings and X-raying convex bodies of constant width
by: Bondarenko, A., et al.
Published: (2020)

Sections and projections of the outer and inner regularizations of a convex body
by: Tziotziou, Natalia
Published: (2025)

Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$
by: Freeman, Nicolas, et al.
Published: (2022)

Illuminating 1-unconditional convex bodies in ${\mathbb R}^3$ and ${\mathbb R}^4$, and certain cases in higher dimensions
by: Sun, Wen Rui, et al.
Published: (2024)

Additive kinematic formulas for convex functions
by: Hug, Daniel, et al.
Published: (2024)

Tightening Inequalities on Volume Extremal $k$-Ellipsoids Using Asymmetry Measures
by: Brandenberg, René, et al.
Published: (2024)

A Comprehensive Definition of the Geometric Mean of Convex Bodies Based on Relations Between Their $p$-Means
by: Brandenberg, René, et al.
Published: (2023)

Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
by: Brandenberg, René, et al.
Published: (2023)

Geometric valuation theory
by: Ludwig, Monika
Published: (2021)

On a generalization of Godbersen's conjecture
by: Kotrbatý, Jan
Published: (2025)

John-type decompositions for affinely-optimal positions of convex bodies
by: Grundbacher, Florian, et al.
Published: (2026)

Kubota-type formulas and supports of mixed measures
by: Hug, Daniel, et al.
Published: (2024)

A note on the affine plank conjecture
by: Bakaev, Egor, et al.
Published: (2026)

Closed polylines with fixed self-intersection index
by: Fomin, Dmitri
Published: (2026)

Lefschetz operators on convex valuations
by: Brauner, Leo, et al.
Published: (2024)

Area and antipodal distance in convex hypersurfaces
by: Dibble, James, et al.
Published: (2026)

Affine Quermassintegrals and Even Minkowski Valuations
by: Hofstätter, Georg C., et al.
Published: (2024)

Inequalities for sections and projections of log-concave functions
by: Tziotziou, Natalia
Published: (2025)

Homothetic packings of centrally symmetric convex bodies
by: Dewar, Sean
Published: (2020)

The Hadwiger theorem on convex functions, II: Cauchy-Kubota formulas
by: Colesanti, Andrea, et al.
Published: (2021)

Convex bodies of constant width with exponential illumination number
by: Arman, Andrii, et al.
Published: (2023)

The Klain approach to zonal valuations
by: Brauner, Leo, et al.
Published: (2024)

From simplex slicing to sharp reverse Hölder inequalities
by: Melbourne, James, et al.
Published: (2025)

Strengthened inequalities for the mean width and the $\ell$-norm
by: Böröczky, Károly J., et al.
Published: (2020)

Centroids of sections of convex bodies and Lusternik-Schnirelmann category
by: Haddad, Julian, et al.
Published: (2025)

Minimal dispersion on the sphere
by: Litvak, Alexander E., et al.
Published: (2025)

Translation invariant area measures on convex bodies
by: Knoerr, Jonas
Published: (2026)

Illumination number of 3-dimensional cap bodies
by: Arman, Andrii, et al.
Published: (2025)

SL($n$) contravariant tensor valuations of small orders
by: Li, Jin, et al.
Published: (2025)

$\operatorname{SL}(n)$ contravariant function-valued valuations on polytopes
by: Tang, Zhongwen, et al.
Published: (2024)

Approximation of the Euclidean ball by polytopes with a fixed number of $k$-faces
by: Hoehner, Steven, et al.
Published: (2025)