Related papers: Note on half-cube embeddings
A middle-cube is an induced subgraph consisting of nodes at the middle two layers of a hypercube. The middle-cubes are related to the well-known Revolving Door (Middle Levels) conjecture. We study the middle-cube graph by completely…
Jorge-Koutrofiotis and Pigola-Rigoli-Setti proved sharp sectional curvature estimates for extrinsically bounded submanifolds. Alias, Bessa and Montenegro showed that these estimates hold on properly immersed cylindrically bounded…
In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].
We establish half-space type results for a class of height-dependent weighted minimal surfaces in $\mathbb{R}^3$, namely critical points of a weighted area functional whose weight depends on the height. When the weight has at most quadratic…
We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.
It is shown that if a $d$-dimensional cube is decomposed into n cubes, the side lengths of which belong to the interval $\left(1-\frac{1}{n^{1/d}+1}, 1\right], then $n$ is a perfect $d$-th power and all cubes are of the same size. This…
A conjectural relationship between the GUE partition function with even couplings and certain special cubic Hodge integrals over the moduli spaces of stable algebraic curves is under consideration.
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].
In this paper we prove the conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily…
This paper considers completions of COMs (complexes oriented matroids) to ample partial cubes of the same VC-dimension. We show that these exist for OMs (oriented matroids) and CUOMs (complexes of uniform oriented matroids). This implies…
We give a sketch for an alternative proof of a recent result by J. Tseng.
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…
We prove that a connected bipartite graph G is a partial cube if and only if the set of attaching points of any copoint of G is convex. A consequence of this result is that any connected bipartite graph with pre-hull number at most 1 is a…
We provide classification results for and examples of half conformally flat generalized quasi Einstein manifolds of signature $(2,2)$. This analysis leads to a natural equation in affine geometry called the affine quasi-Einstein equation…
We show that the computational problem CONSENSUS-HALVING is PPA-complete, the first PPA-completeness result for a problem whose definition does not involve an explicit circuit. We also show that an approximate version of this problem is…
A recent result in [2] on the non-existence of Gauss-Lobatto cubature rules on the triangle is strengthened by establishing a lower bound for the number of nodes of such rules. A method of constructing Lobatto type cubature rules on the…
Optimal weighted Sobolev-Lorentz embeddings with homogeneous weights in open convex cones are established, with the exact value of the optimal constant. These embeddings are non-compact, and this paper investigates the structure of their…
We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated…
We give a simple proof of the following result: There exists a non-convex polyhedron whose surface is isometric to the surface of a cube of smaller volume.
We prove the existence of secondary terms of order $X^{5/6}$ in the asymptotic formulas for the average size of the genus number of cubic fields and for the number of cubic fields with a given genus number, establishing improved error…