arXiv research

Complete Finsler spaces with negative Ricci curvature are reversible.

Study of Schwarzian derivative on Finsler manifolds with constant curvature.

We derive extrinsic curvature estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature.

We study Christoffel and Darboux transforms of discrete isothermic nets in 4-dimensional Euclidean space: definitions and basic properties are derived. Analogies with the smooth case are discussed and a definition for discrete Ribaucour congruences is given. Surfaces of constant mean curvature are special among all iso…

We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. As applications, constant curvature manifolds, Einstein manifolds and Ricci parallel manifolds are identified, respectively, with different integral-differential formulas and semigroup inequaliti…

In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a $C^0$ bound for the Kähler potential. We also discuss some local versions of these estimates which can be of independent interest.

A new option pricing model handles non-constant risk aversion and transaction costs.

Sharp mapping properties and regularization for X-ray transform on disks of constant curvature.

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S^3. The application of the Sym formula …

In this work we derive an approximated no-arbitrage market valuation formula for Constant Maturity Credit Default Swaps (CMCDS). We move from the CDS options market model in Brigo (2004), and derive a formula for CMCDS that is the analogous of the formula for constant maturity swaps in the default free swap market unde…

We derive intrinsic curvature and radius estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature and apply these estimates to study the global geometry of complete surfaces embedded in $\mathbb{R}^3$ with nonzero constant mean curvature.

We relate in this note the classical Schwarzian derivative to the curvature of time-like curves in Lorentz surfaces of constant curvature.

Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h).

Kosmann-Lie derivatives in the bundle of Weyl spinors are considered. It is shown that the basic spin-tensorial fields of this bundle are constants with respect to these derivatives.

Local deformations of solutions to open PDEs can be extended globally if derivatives are constant along a subset.

The paper derives height estimates for surfaces with constant curvature in warped product spaces.

In this note under a crucial technical assumption we derive a differential equality of the Yamabe constant $\mathcal{Y} (g (t))$ where $g (t)$ is a solution of the Ricci flow on a closed manifold.

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fract…

The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved that all the nonsingular pairs of compatible metrics of constant Riemannian curvat…

In this paper we study the behavior of the scalar curvature $S$ of a complete hypersurface immersed with constant mean curvature into a Riemannian space form of constant curvature, deriving a sharp estimate for the infimum of $S$. Our results will be an application of a weak Omori-Yau maximum principle due to Pigola, R…

The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the market for financial derivatives with simple structure in time-direction. However, extending the model to the case of time-…

We consider a market consisting of one safe and one risky asset, which offer constant investment opportunities. Taking into account both proportional transaction costs and linear price impact, we derive optimal rebalancing policies for representative investors with constant relative risk aversion and a long horizon.

In this paper, we derive curvature estimates for strongly stable hypersurfaces with constant mean curvature immersed in $\mathbb{R}^{n+1}$, which show that the locally controlled volume growth yields a globally controlled volume growth if $\partial M=\emptyset$. Moreover, we deduce a Bernstein-type theorem for complete…

We show that the systolic constant, the minimal entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental group of order two (modulo the value on the real…

The study explores metrics with constant curvature on compact manifolds.

Derives stability for curvature measure near constant density, proving dual Minkowski problem solutions.

We derive a correspondence between (Lorentzian) harmonic maps into the pseudosphere $S_1^2$, with appropriate regularity conditions, and certain connection 1-forms. To these harmonic maps, we associate a representation of type Weierstrass, and we apply it to construct timelike surfaces with constant mean curvature.

We show that any $k$ Osserman Lorentzian algebraic curvature tensor has constant sectional curvature and give an elementary proof that any local 2 point homogeneous Lorentzian manifold has constant sectional curvature. We also show that a Szabó Lorentzian covariant derivative algebraic curvature tensor vanishes.

We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give a tensor characterization for such manifolds. We prove that all rotational hyper…

Derives pricing formulas for liquidity tokens in CPMMs, showing riskless growth.

Paper derives uniform error bounds for Gaussian process regression for safer control applications.

This paper proposes a Monte Carlo technique for pricing the forward yield to maturity, when the volatility of the zero-coupon bond is known. We make the assumption of deterministic default intensity (Hazard Rate Function). We make no assumption on the volatility of the yield. We actually calculate the initial value of …

Study on generalized derivations in polynomial vector fields Lie algebras.

Derives explicit investment strategy with random endowment.

Curvature estimates prove existence of smooth hypersurfaces in hyperbolic space.

The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. Many long-term correlated time series in real systems contain various trends. We investigate the effects of polynomial trends on the scaling behaviors and the performa…

Study on warped product Yamabe solitons with constant fiber curvature.

The paper studies geometric constants under modified Ricci flows with variable parameters.

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discre…

In this letter we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth order curvature invariants expressed as polynomials in $Λ$, the cosmological constant. Using this invariant des…

We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module of derivations into free modules; [2] the existence of a measurable differentiable structure assuming that one can control the pointwise up…

New statistical manifolds derived from identity map biharmonicity.

The paper bounds eigenvalues of the Jacobi operator and derives rigidity results for CMC hypersurfaces.

We derive various inequalities involving the intersection number of the curves contained in geodesics and tight geodesics in the curve graph. While there already exist such inequalities on tight geodesics, our method applies in the setting of geodesics. Furthermore, the method gives inequalities with a uniform constant…

Study on CFMMs pricing and hedging, developing models for LP and derivatives valuation.

We construct smooth Riemannian metrics with constant scalar curvature on each Hirzebruch surface. These metrics respect the complex structures, fiber bundle structures, and Lie group actions of cohomogeneity one on these manifolds. Our construction is reduced to an ordinary differential equation called Duffing equation…

Study on surfaces in Heisenberg group with constant mean curvature.

For a convex domain $D$ bounded by the hypersurface $\partial D$ in a space of constant curvature we give sharp bounds on the width $R-r$ of a spherical shell with radii $R$ and $r$ that can enclose $\partial D$, provided that normal curvatures of $\partial D$ are pinched by two positive constants. Furthermore, in the …