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.
Existence proved for static vacuum extensions near Schwarzschild spheres.
Paper defines Bartnik mass for hyperbolic extensions and proves staticity.
Extends static vacuum metrics with specific boundary conditions.
Simple proof for sphere mass calculation.
We investigate Bartnik's static metric extension conjecture under the additional assumption of axisymmetry of both the given Bartnik data and the desired static extensions. To do so, we suggest a geometric flow approach, coupled to the Weyl-Papapetrou formalism for axisymmetric static solutions to the Einstein vacuum e…
Proves existence of static vacuum metrics with specific boundary data.
We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial existence result is obtained, giving a partial resolution of a conjecture of Bartnik …
Paper proves rigidity of static manifolds and applies to metric extensions.
Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik \cite{Bartnik_energy}. We show that, for any metric on that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists …
Maximizes capacity of extensions with fixed boundary data.
Local well-posedness proved for Bartnik static extension near Schwarzschild spheres.
Analyzing static solutions in Finsler gravity, extending known results.
New static vacuum metrics confirmed for near Euclidean boundary data.
Paper analyzes Bartnik's quasi-local mass conjectures and their validity.
A complete characterization is obtained of the asymptotic behavior of solutions of the static vacuum Einstein equations which have a (pseudo)-compact horizon or boundary and are complete away from the boundary. It is proved that the time-symmetric space-like hypersurface has only finitely many ends, each of which is ei…
Estimates mass of static vacuum metrics with small Bartnik data.
Develops a hedging method for multi-asset derivatives with correlation risk.
Given a Riemannian 3-ball of non-negative scalar curvature, Bartnik conjectured that admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined b…
Inspired by the work of Chen-Zhang \cite{Chen-Zhang}, we derive an evolution formula for the Wang-Yau quasi-local energy in reference to a static space, introduced by Chen-Wang-Wang-Yau \cite{CWWY}. If the reference static space represents a mass minimizing, static extension of the initial surface , we observe that …
It is well known that any sufficiently regular one-dimensional payoff function has an explicit static hedge by bonds, forward contracts and lots of vanilla options. We show that the natural extension of the corresponding representation leads to a static hedge based on the same instruments along with traffic light optio…
We propose algorithms for online principal component analysis (PCA) and variance minimization for adaptive settings. Previous literature has focused on upper bounding the static adversarial regret, whose comparator is the optimal fixed action in hindsight. However, static regret is not an appropriate metric when the un…
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier options. For getting the static hedging formula, the underlying process needs to have…
Paper proposes a new DRL algorithm optimizing Spectral Risk Measures for better risk management.
A new algorithm reduces memory usage for deep learning models.
Optimizes nonconvex optimization by converting it to static regret minimization.
In this paper we study the implications of contingent payments on the clearing wealth in a network model of financial contagion. We consider an extension of the Eisenberg-Noe financial contagion model in which the nominal interbank obligations depend on the wealth of the firms in the network. We first consider the prob…
Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.
Attack graphs are a powerful tool for security risk assessment by analysing network vulnerabilities and the paths attackers can use to compromise network resources. The uncertainty about the attacker's behaviour makes Bayesian networks suitable to model attack graphs to perform static and dynamic analysis. Previous app…
The paper analyzes risk measures and optimal reserve allocation strategies.
We solve Bartnik's stationary extension problem near Schwarzschild spheres.
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a "sequentialized" version of any static kernel. The…
We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warpin…
Study of 3D vacuum static spaces with specific curvature properties.
New rigidity theorem on static manifolds with boundary.
In the thesis at hand we give a comprehensive discussion of basic problems for generalized Maxwell equations with mixed boundary conditions using the calculus of alternating differential forms on Riemannian manifolds of arbitrary dimension. We prove compactness results, Hodge decompositions and Poincare type estimates.…
Geometric inequalities for static convex domains in hyperbolic space proved.
The paper classifies vacuum static spaces with harmonic curvature.
The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.
The study proves geometric inequalities for static convex domains in static rotationally symmetric spaces.
Proves equality in Minkowski inequality for static, flat manifolds.
We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sha…
Paper derives Riccati equation for static spaces and proves its applications.
We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The concept of semi-static completeness is introduced: it corresponds to having exact re…
In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum…
Study on stellar models' topology and mass using minimal surfaces.
Classifies vacuum static spaces with harmonic curvature.
Paper proves a rigidity result for static perfect fluids.