Výsledky vyhledávání - "Michael Gene Dobbins"

Completeness for the Complexity Class $$\forall \exists \mathbb {R}$$ and Area-Universality

Autor: Michael Gene Dobbins, Linda Kleist, Tillmann Miltzow, Paweł Rzążewski

Publikováno v: Discrete & Computational Geometry.

Exhibiting a deep connection between purely geometric problems and real algebra, the complexity class $\exists \mathbb{R}$ plays a crucial role in the study of geometric problems. Sometimes $\exists \mathbb{R}$ is referred to as the 'real analog' of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::73cf831aeda8a121e07bd5927e60b70f
https://doi.org/10.1007/s00454-022-00381-0

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Shadows of a Closed Curve

Autor: Heuna Kim, Michael Gene Dobbins, Edgardo Roldán-Pensado, Luis Montejano

Publikováno v: International Mathematics Research Notices. 2020:1992-2006

A shadow of a geometric object A in a given direction v is the orthogonal projection of A on the hyperplane orthogonal to v. We show that any topological embedding of a circle into Euclidean d-space can have at most two shadows that are simple paths

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d9a6a3c04ede77e4cc1db25b2f590ca9
https://doi.org/10.1093/imrn/rny068

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Antiprismlessness, or: Reducing Combinatorial Equivalence to Projective Equivalence in Realizability Problems for Polytopes

Autor: Michael Gene Dobbins

Publikováno v: Discrete & Computational Geometry. 57:966-984

This article exhibits a 4-dimensional combinatorial polytope that has no antiprism, answering a question posed by Bernt Lindstrom. As a consequence, any realization of this combinatorial polytope has a face that it cannot rest upon without toppling o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fc4a92b671e9f151decd22576dd413a1
https://doi.org/10.1007/s00454-017-9874-y

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The Inverse Kakeya Problem

Autor: Otfried Cheong, Michael Gene Dobbins, Sergio Cabello

We prove that the largest convex shape that can be placed inside a given convex shape $$Q \subset \mathbb {R}^{d}$$ in any desired orientation is the largest inscribed ball of Q. The statement is true both when “largest” means “largest volume�

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08d5a0d98ec4944c385a31bc6bb45abf
http://arxiv.org/abs/1912.08477

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$$\forall \exists \mathbb {R}$$∀∃R-Completeness and Area-Universality

Autor: Michael Gene Dobbins, Paweł Rzążewski, Linda Kleist, Tillmann Miltzow

Publikováno v: Graph-Theoretic Concepts in Computer Science ISBN: 9783030002558

In the study of geometric problems, the complexity class $\exists \mathbb {R}$ plays a crucial role since it exhibits a deep connection between purely geometric problems and real algebra. Sometimes $\exists \mathbb {R}$ is referred to as the “r

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fc79ccaad7cded334b1022cbc3901d89
https://doi.org/10.1007/978-3-030-00256-5_14

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Barycenters of points in polytope skeleta

Autor: Florian Frick, Michael Gene Dobbins

The first author showed that for a given point $p$ in an $nk$-polytope $P$ there are $n$ points in the $k$-faces of $P$, whose barycenter is $p$. We show that we can increase the dimension of $P$ by $r$, if we allow $r$ of the points to be in $(k+1)$

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c7fe03785ee56326b84474a0bef8dbf6

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Realizability of Polytopes as a Low Rank Matrix Completion Problem

Autor: Michael Gene Dobbins

Publikováno v: Discrete & Computational Geometry. 51:761-778

This article gives necessary and sufficient conditions for a relation to be the containment relation between the facets and vertices of a polytope. Also given here, are a set of matrices parameterizing the linear moduli space and another set paramete

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed54b11a692c6bbc3533f0c5bf9478fa
https://doi.org/10.1007/s00454-014-9599-0

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A point in a $$nd$$ n d -polytope is the barycenter of $$n$$ n points in its $$d$$ d -faces

Autor: Michael Gene Dobbins

Publikováno v: Inventiones mathematicae. 199:287-292

Using equivariant topology, we prove that it is always possible to find $$n$$ points in the $$d$$ -dimensional faces of a $$nd$$ -dimensional convex polytope $$P$$ so that their center of mass is a target point in $$P$$ . Equivalently, the $$n$$ -fol

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5e90a754bcaaa7a79a1f660777b416da
https://doi.org/10.1007/s00222-014-0523-2

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Regular systems of paths and families of convex sets in convex position

Autor: Andreas F. Holmsen, Alfredo Hubard, Michael Gene Dobbins

Publikováno v: Transactions of the American Mathematical Society
Transactions of the American Mathematical Society, American Mathematical Society, 2015, ⟨10.1090/tran/6437⟩
Transactions of the American Mathematical Society, 2015, ⟨10.1090/tran/6437⟩

International audience; In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamil

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04d4120d19ebb9ee963ef32edfb1fc54
https://hal.archives-ouvertes.fr/hal-01286261

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