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.
New geometric measure simplifies complex analysis.
New Crofton formulae derived from existing ones.
Explains geometric inequalities for minimal hypersurfaces.
In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distri…
Study geometric inequalities for quasi-Einstein manifolds using new formulas.
New formulas link string bordism to integers.
Study applies Huisken formula to mean curvature flow in Ricci soliton background.
Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The formula is based on the fact that the space of similarity classes of triangles …
The paper simplifies FLRW photon propagators using geometric embeddings.
Paper proposes a closed-form formula for geometric Istanbul call options.
We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the 2-sphere (whose holonomy is seen to be responsible for the geometric phase). We also give an approximate geometric interpretation of the geometri…
Geometric formula derived for Lefschetz pairing on Γ-proper manifolds.
Study on hyperbolic manifolds with special boundaries.
The paper calculates the full asymptotics of analytic torsions for compact orbifolds.
Study curvature and torsion in Gaussian distribution's dual coordinate system.
The paper extends geometric inequalities from Euclidean space to Riemannian manifolds.
We give a direct geometric proof of a Danilov-type formula for toric origami manifolds by using the localization of Riemann-Roch number.
The paper derives formulas for pricing geometric Asian options in the Volterra-Heston model.
Proves modular functors for SO(3) have integral Hodge structures.
The paper studies geometric constants under modified Ricci flows with variable parameters.
Formula connects curvature to volume in special geometric spaces.
New formulas for measuring geometric properties of definable sets.
In this paper, we establish an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds by using the Mathai-Quillen's superconnection formalism, in which no extra vector field is involved. Furthermore, we prove a more general Lichnerowicz formula in this direction through a geometric localization procedure.
We establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map.
We suggest an algorithm allowing to obtain some new integral-geometric formulae from the existing formulae of Crofton type. These new formulae are applied to get smooth versions of BKK theorem. The algorithm is based on the calculations in the ring of normal densities on a manifold.
Formula removes geometric patterns from random hyperbolic surfaces.
Intermediate logic of all convex polyhedra is axiomatized.
We give three formulas expressing the Smale invariant of an immersion f of a (4k-1)-sphere into (4k+1)-space. The terms of the formulas are geometric characteristics of any generic smooth map g of any oriented 4k-dimensional manifold, where g restricted to the boundary is an immersion regularly homotopic to f in (6k-1)…
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
Geometrically reformulates the Laplace method for optimal transport.
We provide a geometric construction of the boundary states for handlebodies which we in turn use to give a geometric formula for the Witten-Reshetikhin-Turaev quantum invariants. We then analyze the asymptotics of this invariant in the special case of a three manifold given by 1-surgery on a knot and we show that if th…
The Weitzenböck curvature operators are the curvature terms of order zero that appear in the well known classical Weitzenböck formula. In this paper, we use the formalism of double forms to prove a simple formula for this operators and to study their geometric properties.
Formula for the force field of Newtonian dynamical systems admitting the normal shift of hypersurfaces in Riemannian manifolds is considered. Problem of globalization for geometric structures associated with this formula is studied.
We prove a monotonicity formula for mean curvature flow with surgery. This formula differs from Huisken's monotonicity formula by an extra term involving the mean curvature. As a consequence, we show that a surgically modified flow which is sufficiently close to a smooth flow in the sense of geometric measure theory is…
We give an explicit geometric formula for the twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. Combining with the twisted trace formula, we can evaluate the equivariant trace of the heat operators of the Laplacians on a compact locally symmetric space. In particular, we revi…
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of genera…
We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achie…
Construct geometric interpretation of Heston model using group quantization.
This study presents a long-term alternative formula for stock price variation described by a geometric Brownian motion on the basis of median instead of mean or expected values. The proposed method is motivated by the observation made in remote fields, where optimality of bet-hedging or diversification strategies is ex…
The paper develops formulas for hyperbolic simplices based on edge lengths.
We introduce the notion of partial presimplicial set and construct its geometric realization. We show that any semiadequate diagram yields a partial presimplicial set leading to a geometric realization of the almost-extreme Khovanov homology of the diagram. We give a concrete formula for the homotopy type of this geome…
We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. I…
Formula conjectured for rational cuspidal curves in projective plane.
Study extends geodesic curvature formula to higher dimensions.
We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability tensors of the distributions. The formulas under some conditions yield splitting…
We derive a representation formula for the tensorial wave equation $\Box_\bg φ^I=F^I$ in globally hyperbolic Lorentzian spacetimes $(\M^{2+1}, \bg)$ by giving a geometric formulation of the method of descent which is applicable for any dimension.