The upper bound conjecture for arrangements of half-spaces.
The Upper Envelope of Voronoi Surfaces and Its Applications.
The vanishing of the cohomology of the Orlik-Solomon algebras.
The View-Obstruction Problem for Spheres in ...5.
The Weakly Neighborly Polyhedral Maps on the 2-Manifold with Euler Characteristic -1.
The Worm Problem of Leo Moser.
Théorème d'approximation et espaces de Hopf.
Theorems of the alternative for cones and Lyapunov regularity of matrices
Standard facts about separating linear functionals will be used to determine how two cones and and their duals and may overlap. When is linear and and are cones, these results will be applied to and , giving a unified treatment of several theorems of the alternate which explain when contains an interior point of . The case when is the space of Hermitian matrices, is the positive semidefinite matrices, and yields new and known results about the existence of block diagonal...
Theorems on equipartition of a continuous mass distribution.
Theorems on the Existence of Separating Surfaces.
There Exist 6n/13 Ordinary Points.
There is no cogenerator of totally convex spaces
Thin-shell concentration for convex measures
We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.
Three-dimensional pseudomanifolds on eight vertices.
Tietze's convexity theorey for lattices and semilattices.
Tight and 0-Tight Polyhedral Embeddings of Surfaces.
Tight embeddings of simply connected 4-manifolds.
Tile-transitive partial tilings of the plane.
Tiling and spectral properties of near-cubic domains
We prove that if a measurable domain tiles ℝ or ℝ² by translations, and if it is "close enough" to a line segment or a square respectively, then it admits a lattice tiling. We also prove a similar result for spectral sets in dimension 1, and give an example showing that there is no analogue of the tiling result in dimensions 3 and higher.
Tiling Polygons with Parallelograms.