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.
The paper generalizes CR invariants using renormalized characteristic forms.
We derive variational formulas for the total Q-prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold. We also show that the total Q-prime curvature agrees with the renormalized volume of such domains with respect to the complete Einstein-Kähler metric. In the appendix, by Rod Gove…
The -prime curvature is a local invariant of pseudo-Einstein contact forms on integrable strictly pseudoconvex CR manifolds. The transformation law of the -prime curvature under scaling is given in terms of a differential operator, called the -prime operator, acting on the space of CR pluriharmonic functions. …
The Q-curvature has been playing a central role in conformal geometry since its discovery by T. Branson. It has natural analogy in CR geometry, however, the CR Q-curvature vanishes on the boundary of a strictly pseudoconvex domain in C^{n+1} with a natural choice of contact form. This fact enables us to define a "secon…
We establish an algorithm which computes formulae for the CR GJMS operators, the -operator, and the -curvature in terms of CR tractors. When applied to torsion-free pseudo-Einstein contact forms, this algorithm both gives an explicit factorisation of the CR GJMS operators and the -operator…
The study proves CR structures on specific three-manifolds are equivalent to standard structures.
We prove that the total CR -curvature vanishes for any compact strictly pseudoconvex CR manifold. We also prove the formal self-adjointness of the -operator and the CR invariance of the total -curvature for any pseudo-Einstein manifold without the assumption that it bounds a Stein manifold.
We give an integral formula for the total -curvature of a three-dimensional CR manifold with positive CR Yamabe constant and nonnegative Paneitz operator. Our derivation includes a relationship between the Green's functions of the CR Laplacian and the -operator.
We construct contact forms with constant -curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by minimizing the CR analogue of the -functional from conformal geometry. Two crucial st…
We construct contact forms with constant -curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by minimizing the CR analogue of the -functional from conformal geometry. Two crucial st…
The theory of ambient spaces is useful to define CR invariant objects, such as CR invariant powers of the sub-Laplacian, the -prime operators, and -prime curvature. However in general, it is difficult to write down these objects in terms of the Tanaka-Webster connection. In this paper, we give those explicit form…
In this paper we study the problem of prescribing the -curvature on pseudo-Einstein CR 3-manifolds. In the first stage we study the problem in the compact setting and we show that under natural assumptions, one can prescribe any positive CR pluriharmonic function. In the second stage we study the probl…
In this paper one studies the distribution of log-returns (tick-by-tick) in the Lisbon stock market and shows that it is well adjusted by the solution of the equation, {}, which corresponds to a generalization of the differential …
The nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this nonnegativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the CR Yamabe problem for embeddable CR manifolds. We also show the existence of a co…
We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space with prime is completely characterized by its Dirac spectrum in the class of all lens spaces.
We study different notions of Riemannian curvatures: The -curvatures which interpolate between the scalar curvature and the sectional curvature, the Gauss-Bonnet-Weyl curvatures form another interpolation from the scalar curvature to the Gauss-Bonnet integrand. We bring out the -curvatures, which incorporate …
Paper establishes a relation between Berwald scalar curvature and S-curvature.
New scalar curvature defined from Ollivier-Ricci curvature for graphs.
We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyper-pseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with co…
New metric with negative curvature found near positive-curvature spaces.
Study examines preservation of curvature-adaptedness during mean curvature flow.
Paper explores entropic curvature in Markov chains, comparing it to other curvatures.
The paper studies Berwald scalar curvature properties in Finsler geometry.
The paper studies Finsler manifolds with a new curvature concept.
New proof shows holomorphic sectional curvature fully determines curvature tensor.
Given a compact four dimensional smooth Riemannian manifold with smooth boundary, we consider the evolution equation by -curvature in the interior keeping the -curvature and the mean curvature to be zero and the evolution equation by -curvature at the boundary with the condition that the -curvature …
The curvature-dimension condition implies a new weighted scalar curvature.
Compact shrinkers with curvature pinching conditions proven.
Study geodesic curvature of logarithmic spirals on curved surfaces.
Study on singularity behavior of mean curvature flow with bounded curvature and index.
New curvature definitions for networks simplify complex computations.
Study on curvature in finitely generated groups, showing positive curvature in specific cases.
Introduces new curvature concept for Kähler manifolds.
The paper studies Kropina metrics with a specific curvature property.
We introduce a natural extension of the metric tensor and the Hodge star operator to the algebra of double forms to study some aspects of the structure of this algebra. These properties are then used to study new Riemannian curvature invariants, called the -curvatures. They are a generalization of the -curvat…
The paper examines geometric properties of a unique spacetime model.
Quantitative estimate for curvature in mean curvature flow.
Study on hypersurfaces with specific curvature conditions.
New insights into SGD and generalization via shift-curvature and bias-curvature mechanisms.
Lower bounds on curvature integral for manifolds with curvature constraints.
Solves curvature problems on manifolds with negative curvature.
The paper finds and analyzes the Funk-Finsler structure in constant curvature spaces.
The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an open subset in R^n with negative flag curvature and constant S-curvature. In th…
Paper estimates curvature of convex hypersurfaces with prescribed curvature.
A complete surface of constant mean curvature 1 (CMC-1) in hyperbolic 3-space with constant curvature -1 has two natural notions of "total curvature"-- one is the total absolute curvature which is the integral over the surface of the absolute value of the Gaussian curvature, and the other is the dual total absolute cur…
Curvature estimates prove existence of smooth hypersurfaces in hyperbolic space.
Study shows no large mean curvature fill-ins for nonnegative scalar curvature.
The abstract finds conditions for creating curves of constant curvature.