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.
Study geometric properties of surfaces with specific formulae.
Formula calculates Riemann-Roch number for singular symplectic quotients.
The paper derives Gauss-Bonnet formulas for mappings between surfaces with boundary.
Study on conical singularities in 2D surfaces, deriving Polyakov formulas.
Wave trace singularity formula for fibre bundles generalizes Poisson summation.
We prove a global residual formula in terms of logarithmic indices for one-dimensional holomorphic foliations, with isolated singularities, and logarithmic along normal crossing divisors. We also give a formula for the total sum of the logarithmic indices if the singular set of the foliation is contained in the invaria…
In this note, we prove a quantization formula for singular reductions. The main result is obtained as a simple application of an extended quantization formula proved in [TZ2].
Generalizes Gauss-Bonnet to metrics with logarithmic singularities.
Formula calculates homology groups of Milnor fibres for real hypersurface singularities.
Paper develops techniques for singular metrics on vector bundles.
We generalise the classical Chern-Gauss-Bonnet formula to a class of 4-dimensional manifolds with finitely many conformally flat ends and singular points. This extends results of Chang-Qing-Yang in the smooth case. Under the assumptions of finite total Q curvature and positive scalar curvature at the ends and at the si…
We present and prove Polyakov-Alvarez type comparison formulas for the determinants of Friederichs extensions of Laplacians corresponding to conformally equivalent metrics on a compact Riemann surface with conical singularities. In particular, we find how the determinants depend on the orders of conical singularities. …
We study singularities of surfaces which are given by Kenmotsu-type formula with prescribed unbounded mean curvature.
This paper proves geodesic curvature measures are bounded for curves near cross cap singularities.
Study calculates ring structure in instanton homology for a surface with points.
Abstract: Characterizes frontals and wavefronts with formulas.
The paper studies singularities in discrete indefinite affine minimal surfaces.
We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions and study singularities which appear in this representation formula. As a result, it follows that cuspidal cross caps never appear as the singularities on indefinite improper affine spheres and so…
Study on a specific obstruction in four-dimensional geometry.
Formula counts rational curves with a specific singular point in projective space.
Formula proves Euler characteristic of singularized surfaces.
In a previous article, we generalised the classical four-dimensional Chern-Gauss-Bonnet formula to a class of manifolds with finitely many conformally flat ends and singular points, in particular obtaining the first such formula in a dimension higher than two which allows the underlying manifold to have isolated conica…
We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator fo…
Paper finds formulas for minimizing perimeter in special spaces, proving key dimensions and existence.
Paper provides a formula for translating solitons and singular minimal surfaces.
We show a natural relation between the monodromy formula for focus-focus singularities of integrable Hamiltonian systems and a formula of Duistermaat-Heckman, and extend the main results of our previous note on focus-focus singularities ($\bbS^1$-action, monodromy, and topological classification) to the degenerate case…
Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularities. As corollaries we obtain an algebraic formula for the Euler characteristic of the fibres …
Mathematical formulas for elliptic curve integrals solve anomaly equations.
We derive a cut-and-paste surgery formula of Seiberg--Witten invariants for negative definite plumbed rational homology 3-spheres. It is similar to (and motivated by) Okuma's recursion formula [arXiv:math.AG/0610464, 4.5] targeting analytic invariants of splice quotient singularities. The two formulas combined provide …
Study on contact Hamiltonian functions for singular contact structures.
The study examines Riemannian surfaces with simple singularities.
Study conically singular instantons over SU(3)-manifolds, proving existence and dimension formulas.
For two complex vector bundles admitting a homomorphism between them, a Poincaré-Hopf formula for the difference of the Chern character numbers of these two vector bundles with isolated singularities is established by Huitao Feng, Weiping Li and Weiping Zhang. This article extend their reslut about Poincaré-Hopf type f…
In this paper, we introduce a monotonicity formula for the mean curvature flow. We also apply this monotonicity formula to study the asymptotic behavior of eternal solutions.
We extend Guillemin's formula for Kaehler potentials on toric manifolds to singular quotients of C^N and CP^N.
Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With certain restrictions on the metric, we establish that the spectrum is discrete …
We give an explicit formula for singular surfaces of revolution with prescribed unbounded mean curvature. Using it, we give conditions for singularities of that surfaces. Periodicity of that surface is also discussed.
The paper is devoted to differential geometry of singular distributions (i.e., of varying dimension) on a Riemannian manifold. Such distributions are defined as images of the tangent bundle under smooth endomorphisms. We prove the novel divergence theorem with the divergence type operator and deduce the Codazzi equatio…
The paper studies how surfaces move by mean curvature flow and what happens at singular points.
We study the Euler obstruction of essentially isolated determinantal singularities (EIDS). The EIDS were defined by W. Ebeling and S. Gusein-Zade, as a generalization of isolated singularity. We obtain some formulas to calculate the Euler obstruction for the determinantal varieties with singular set an ICIS.
Study nondegenerate singularities in mean curvature flow.
Study vector fields with complex singularities, proving bounds and formulas.
We construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. The first is an understanding of how the components of the invariant change when we remove a curve from the …
Canonical bundle formula due to Kawamata and others has played fundamental roles in algebraic geometry. We show that the canonical bundle formula has analytic characterization in terms of fiberwise integration, which confirms a folklore conjecture. The proof uses metrics and the valuative equivalence of plurisubh…
The paper extends Weyl formulae for Schrödinger operators with singular potentials.
We prove residual formulas for vector fields defined on compact complex orbifolds with isolated singularities and give some applications of these on weighted projective spaces.
The paper studies Gauss sums and their applications in algebra and topology.
Study of mean curvature flows with conical singularities using mathematical techniques.