A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New finding links hyperbolic manifold systolic volume to triangulation complexity.
Integral filling volume of mapping tori grows sublinearly with complexity.
Proves volume conjecture for twist knots using complex analysis.
Minimal volume entropy vanishes or is positive under certain fiber growth conditions.
Estimates Kähler metrics with noncollapsing volume under complex Monge-Ampère constraints.
We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal volume are the two smallest arithmetic complex hyperbolic 2-orbifolds. We then show that every arithmetic cusped complex hyperbolic 2-manifold of minimal volume covers one of these two orbifolds. We also give all minimal volume manifolds that…
In this paper, we prove that the systolic volume of a closed aspherical 3-manifold is bounded below in terms of complexity. Systolic volume is defined as the optimal constant in a systolic inequality. Babenko showed that the systolic volume is a homotopy invariant. Moreover, Gromov proved that the systolic volume depen…
We compare the volume of a hyperbolic 3-manifold of finite volume and the complexity of its fundamental group.
Study intrinsic volume forms on complex hypersurfaces.
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present complementing topological conditions expressed in terms of the growth of the fundamental g…
We try to give a cluster algebraic interpretation of complex volume of knots. We construct the R-operator from the cluster mutations, and we show that it is regarded as a hyperbolic octahedron. The cluster variables are interpreted as edge parameters used by Zickert in computing complex volume.
In the paper we define a "volume" for simplicial complexes of flag tetrahedra. This generalizes and unifies the classical volume of hyperbolic manifolds and the volume of CR tetrahedra complexes. We describe when this volume belongs to the Bloch group. In doing so, we recover and generalize results of Neumann-Zagier, N…
The goal of this paper is to study the geometry of cusped complex hyperbolic manifolds through their compactifications. We characterize toroidal compactifications with non-nef canonical divisor. We derive effective very ampleness results for toroidal compactifications of finite volume complex hyperbolic manifolds. We e…
We construct an explicit lower bound for the volume of a complex hyperbolic orbifold that depends only on dimension.
In this paper, we prove an equality which involves Reidemeister torsion, complex volume, and Zograf infinite product for closed hyperbolic 3-manifolds.
Study minimal surfaces in complex hyperbolic space, linking entropy and volume.
The study links Ricci curvature and convexity in complex tori.
The period for a compact Riemann surface, defined by the integral of differential 1-forms, is a classical complex analytic invariant, strongly related to the complex structure of the surface. In this paper, we treat another complex analytic invariant called the pointed harmonic volume. As a natural extension of the per…
In this paper, we prove an equality which involves Reidemeister torsion, complex volume, and Zograf infinite product for hyperbolic 3-manifolds with cusps.
Essential minimal volume bounds for Einstein 4-manifolds.
Estimates Schwarzian derivative on long complex projective tubes.
For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete Kähler metric of Fefferman. We compute the conformal anomaly in complex dimension two and apply the result to derive a renormalized Chern--Gauss--Bonnet formula. Relations between…
Volume is a natural measure of complexity of a Riemannian manifold. In this survey, we discuss the results and conjectures concerning n-dimensional hyperbolic manifolds and orbifolds of small volume.
Study volumes of Bott-Chern classes on complex manifolds.
Yokota suggested an optimistic limit method of the Kashaev invariants of hyperbolic knots and showed it determines the complex volumes of the knots. His method is very effective and gives almost combinatorial method of calculating the complex volumes. However, to describe the triangulation of the knot complement, he re…
Study minimal volume entropy for free-by-cyclic groups and 2D right-angled Artin groups.
Complex - symbols relate to hyperbolic tetrahedron volumes and determinants.
We propose a method to compute complex volume of 2-bridge link complements. Our construction sheds light on a relationship between cluster variables with coefficients and canonical decompositions of link complements.
We study the asymptotic behavior of volume forms on a degenerating family of compact complex manifolds. Under rather general conditions, we prove that the volume forms converge in a natural sense to a Lebesgue-type measure on a certain simplicial complex. In particular, this provides a measure-theoretic version of a co…
In this paper we get an explicit lower bound for the radius of a Bergman ball contained in the Dirichlet fundamental polyhedron of a torsion-free discrete group acting on complex hyperbolic space. Consequently the volume of all complex hyperbolic n-manifolds is bounded below by the volume of this bal…
In this paper, we prove that principal circle bundles over the complex projective space equipped with the standard Sasakian structures are volume rigid among all -contact manifolds satisfying positivity conditions of tensors involing the Tanaka-Webster curvature.
Efficiently samples arbitrary compact bodies with polynomial complexity.
Loosely speaking, the Volume Conjecture states that the limit of the n-th colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex n-th root of unity is a sequence of complex numbers that grows exponentially. Moreover, the exponential growth rate is proportional to the hyperbolic volume of the …
Finite simplicial complexes dominate certain manifolds with a bounded number of simplices.
Study bounds on Monge-Ampère volumes for degenerate complex equations.
The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another complex analytic invariant called the harmonic volume. It is a natural extension o…
Improved lower bounds on 2-bridge link complexity.
We prove a new inequality relating volume to length of closed geodesics on area minimizers for generic metrics on the complex projective plane. We exploit recent regularity results for area minimizers by Moore and White, and the Kronheimer--Mrowka proof of the Thom conjecture.
Constructs simplified or complexified simplicial complexes.
We observe inequalities involving the Herzlich volume of a 4-dimensional asymptotically complex hyperbolic Einstein manifold and its Euler characteristic provided the metrics is either Kaehler or selfdual. In the selfdual case we have to assume furthermore that the Kronheimer-Mrowka invariant is non vanishing.
We prove a conjecture saying that complex projective space has maximal volume (degree) among all toric Kaehler-Einstein manifolds of dimension n. The proof is inspired by our recent work on sharp Moser-Trudinger and Brezis-Merle type inequalities for the complex Monge-Ampere operator, but is essentially self-contained.
This note computes the "renormalized volume" and a renormalizedGauss-Bonnet-Chern formula for the Euler characteristic ofasymptotically complex hyperbolic Einstein (in short: ACHE)4-manifolds.
We introduce a new homology theory of quandles, called simplicial quandle homology, which is quite different from quandle homology developed by Carter et al. We construct a homomorphism from a quandle homology group to a simplicial quandle homology group. As an application, we obtain a method for computing the complex …
We view closed orientable 3-manifolds as covers of S^3 branched over hyperbolic links. For a p-fold cover M \to S^3, branched over a hyperbolic link L, we assign the complexity p Vol(S^3 minus L) (where Vol is the hyperbolic volume). We define an invariant of 3-manifolds, called the link volume and denoted LV, that ass…
Efficient algorithm for sampling from arbitrary compact bodies.
We compute the measure with multiplicity of the set of complex planes intersecting a compact domain in a complex space form. The result is given in terms of the so-called hermitian intrinsic volumes. Moreover, we obtain two different versions for the Gauss-Bonnet-Chern formula in complex space forms. One of them gives …
We study the problem of bounding the number of cusps of a complex hyperbolic manifold in terms of its volume. Applying algebro-geometric methods using Mumford's work on toroidal compactifications and its generalization due to N. Mok and W.-K. To, we get a bound which is considerably better than those obtained previousl…
We calculate the asymptotic behavior of hyperbolic volume and Chern-Simons invariant.