Related papers: Viterbo's conjecture as a worm problem
A gravitational theory of a scalar field non-minimally coupled with torsion and boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these…
A variational formula is derived by combining the Gaussian volume of the epigraph of a convex function $\varphi$ and the perturbation of $\varphi$ via the infimal convolution. This formula naturally leads to a Borel measure on…
J. J. Sylvester's four-point problem asks for the probability that four points chosen uniformly at random in the plane have a triangle as their convex hull. Using a combinatorial classification of points in the plane due to Goodman and…
We present a general conjecture on the divisibility of a certain expression in terms of Kostka numbers and their close variants. This conjecture is closely related to a variant of the period-index problem of noncommutative algebra, with…
In this paper we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V.~Milman regarding the volume of $\partial K+ \partial T$ where $K$ and $T$ are convex bodies, we…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
Our main issue was to understand the connection between \L ukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we define the class of \textit{f}MV-algebras, which are…
A quantum inequality bound on the expectation value of the null-contracted stress tensor in an arbitrary Hadamard state is used to obtain constraints on the geometries of traversable wormholes. Particular attention is given to the wormhole…
The "Mahler volume" is, intuitively speaking, a measure of how "round" a centrally symmetric convex body is. In one direction this intuition is given weight by a result of Santalo, who in the 1940s showed that the Mahler volume is…
We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. Our conjectures are based on experimental data that we derived by developing a numerical linear algebra and distributed…
We present a proposal to include Lorentz-violating effects in gravitational field by means of the Finsler geometry. In the Finsler set up, the length of an event depends both on the point and the direction in the space-time. We briefly…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $n$ independent hyperplanes, and discuss the equality case and the uniqueness of the solution of the related case of the logarithmic Minkowski problem. We also…
A longstanding question in the dual Brunn-Minkowski theory is what are the dual analogues of Federer's curvature measures for convex bodies. The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems,…
We introduce the notion of equiangular tight frames in real symplectic spaces and formulate a conjecture on their existence in terms of the dimension and number of vectors. Our main results shows the "symplectic Zauner's conjecture" is…
This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the…
We explore a natural generalization of systolic geometry to Finsler metrics and optical hypersurfaces with special emphasis on its relation to the Mahler conjecture and the geometry of numbers. In particular, we show that if an optical…
In this note we extend to non trivial Hamiltonian fibrations over symplectically uniruled manifolds a result of Lu's, \cite{Lu}, stating that any trivial symplectic product of two closed symplectic manifolds with one of them being…
In a recent work [2] with Datta, we introduced the mu vector (with respect to a given field) of simplicial complexes and used it to study tightness and lower bounds. In this paper, we modify the definition of mu vectors. With the new…
We develop a variational approach to the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations. Under mild assumptions, we introduce viscosity Mather measures for such partial differential…