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.
Modeling financial system dynamics with interbank flows and borrowing.
We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially symmetric initial surfaces with sufficiently large volume…
Study reveals risks of investing in new crypto-tokens in decentralized exchanges.
Study shows no closed trapped submanifolds can be tangent to certain spacelike hypersurfaces.
Study analyzes household capital risk and poverty trapping, deriving a new function for capital deficit distribution.
We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and hyperbolic 3-space, endowed with their canonical neutral Kaehler structures. We prove that every rank one surface in these four manifolds i…
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increas…
Study of marginally trapped surfaces in a perturbed Schwarzschild spacetime.
The paper introduces canonical parameters for marginally trapped surfaces in Minkowski space.
Generic singularities found in spacetimes with weakly trapped submanifolds.
Study improves curvature estimate for stable marginally outer trapped hypersurfaces with a free boundary.
We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data c…
Wariness affects poverty traps and equilibrium diversity in economic models.
Proves stable smooth minimal hypersurface for trapped region boundary in large dimensional manifolds.
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. In the present paper we find all marginally trapped surfaces with pointwise 1-type Gauss map. We prove that a marginally trapped surface is of pointwise 1-type Gauss map if…
Proves two non-trapping obstacles coincide if scattering rays have similar travelling times or scattering length spectra.
This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers…
Paper proves trapped surface formation for EMCSF system without symmetry assumptions.
Overview of marginally trapped surfaces in various spacetimes.
No trapped surfaces can form under low-regularity bounds in certain spacetimes.
The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the mathematical community, I introduce the generalized idea of trapped submanifold by using t…
Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.
Deep learning system speeds up wildlife species identification from camera trap images.
In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf …
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situatio…
New system studies trapped light paths in Euclidean space.
The paper studies marginally trapped submanifolds in Lorentzian manifolds under null energy condition.
Study shows certain manifolds uniquely determined by X-ray data.
The purpose of the present work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let $(M,g,N)\to\Bm(c)$ be a null hypersurface of a space-time with constant sectional curvature , endowed with a Screen Integrable and Conformal rigging . The (Marginally) Trapped Submanifolds we are intere…
Study on trapped submanifolds in spacetimes, proving rigidity and non-existence results.
Model shows how investment traps wealth across generations.
We show that degenerate horizons exhibit a new trapping effect. Specifically, we obtain a non-degenerate Morawetz estimate for the wave equation in the domain of outer communications of extremal Reissner-Nordstrom up to and including the future event horizon. We show that such an estimate requires 1) a higher degree of…
New proof of trapped surface formation using signature for decay rates.
Study examines how insurance affects households prone to proportional losses, especially those near poverty.
Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal …
We solve the Plateau problem for marginally outer trapped surfaces in general Cauchy data sets. We employ the Perron method and tools from geometric measure theory to force and control a blow-up of Jang's equation. Substantial new geometric insights regarding the lower order properties of marginally outer trapped surfa…
New method shows trapped surfaces form in geodesic foliation.
New integrable systems for marginally trapped surfaces in 4D Lorentz-Minkowski space.
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We introduce meridian surfaces of parabolic type as one-parameter systems of meridians of a rotational hypersurface with lightlike axis in Minkowski 4-space and find their …
Marginally outer trapped surfaces are widely considered as the best quasi-local replacements for event horizons of black holes in General Relativity. However, this equivalence is far from being proved, even in stationary and static situations. In this paper we study an important aspect of this equivalence, namely wheth…
In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem on the topology of black holes). We first prove that an unbounded, stable margi…
Study shows how electromagnetic and gravitational waves can form trapped surfaces.
Study of trapped photons in Kerr spacetime's phase space.
Study rigidity in Penrose's singularity theorem with weakly trapped surfaces.
We give explicit representation formulas for marginally trapped submanifolds of co-dimension two in pseudo-Riemannian spaces with arbitrary signature and constant sectional curvature. This paper is dedicated to the memory of Franki Dillen, 1963-2013.
Klainerman, Luk and Rodnianski derived an anisotropic criterion for formation of trapped surfaces in vacuum, extending the original trapped surface formation theorem of Christodoulou. The effort to understand their result led us to study the intersection of a hyperplane with a lightcone in the Minkowski spacetime. For …
Conformal geodesics can't spiral in Riemannian manifolds.
Study stability and rigidity of axisymmetric marginally outer trapped surfaces.