Abstract
AbstractWe continue the study of intersection bodies of polytopes, focusing on the behavior of IP under translations of P. We introduce an affine hyperplane arrangement and show that the polynomials describing the boundary of $$I(P+t)$$
I
(
P
+
t
)
can be extended to polynomials in variables $$t\in \mathbb {R}^d$$
t
∈
R
d
within each region of the arrangement. In dimension 2, we give a full characterization of those polygons such that their intersection body is convex. We give a partial characterization for general dimensions.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference23 articles.
1. Berlow, K., Brandenburg, M-C., Meroni, C., Shankar, I.: MATHREPO. Mathematical Data and Software. Intersection Bodies of Polytopes.[Online; accessed 21-February-2023]. (2021) url: https://mathrepo.mis.mpg.de/intersection-bodies
2. Berlow, K., Brandenburg, M.C., Meroni, C., Shankar, I.: Intersection Bodies of Polytopes. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 63, 419–439 (2022). https://doi.org/10.1007/s13366-022-00621-7
3. Berck, G.: Convexity of $$L_p$$-intersection bodies. Adv. Math. 222(3), 920–936 (2009). https://doi.org/10.1016/j.aim.2009.05.009
4. Brehm, U.: Convex bodies with non-convex cross-section bodies. Mathematika 46(1), 127–129 (1999). https://doi.org/10.1112/S0025579300007610
5. Breiding, P., Ranestad, K., Weinstein, M.: Critical Curvature of Algebraic Surfaces in Three-Space. arxiv:2206.09130 (2022)
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