Related papers: Marked length varieties and arithmeticity

We consider mixed integer linear sets defined by two equations involving two integer variables and any number of non-negative continuous variables. The non-trivial valid inequalities of such sets can be classified into split, type 1, type…

This paper shows certain classes of metric spaces characterized by volume growth properties of balls can viewed as graphs with infinitesimal edges. Our approach is based on nonstandard analysis.

We introduce a notion of a non-Abelian loop gauge field defined on points in loop space. For this purpose we first find an infinite-dimensional tensor product representation of the Lie algebra which is particularly suited for fields on loop…

We study rigidity on certain K\"ahler manifolds with nonnegative Ricci curvature. Among others things, we show that a complete noncompact K\"ahler surface with nonnegative Ricci curvature, Euclidean volume growth and quadratic curvature…

We find sharp upper bounds for the multiplicities and the numerical values of all the distinct eigenvalues on a surface of revolution diffeomorphic to the sphere.

We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower…

This is a review article on the Bennequin-Birman-Menasco machinery for studying embedded incompressible surfaces in 3-space via their `braid foliations'. Two cases are investigated: case (1) The surface has non-empty boundary; the boundary…

In this paper we characterize logarithmic surfaces which admit K\"ahler-Einstein metrics with negative scalar curvature and small edge singularities along a normal crossing divisor.

In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian…

A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.

We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields…

We give an elementary obstruction to reducibility for knotted surfaces in the four-sphere. As a new application, we construct stably irreducible non-orientable surfaces.

We discuss relations between certain invariants of varieties in positive characteristic, like the a-number and the height of the Artin-Mazur formal group. We calculate the a-number for Fermat surfaces

The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist.

We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…

In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.

We introduce the arithmetic width of a convex body, defined as the number of distinct values a linear functional attains on the lattice points within the body. Arithmetic width refines lattice width by detecting gaps in the lattice point…

In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI…

We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in $\mathbb R^d$. In our setting we allow multiple vertices to be constrained to the same line. Under a mild…

In this paper, we consider non developable ruled surface with spacelike ruling, timelike ruling, respectively. We give the relations between the structure functions with the curvature and torsion of the striction line of the timelike and…