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 spinorial Yamabe problem on product manifolds, proving spike layer solutions.
This paper studies non-compactness in spinorial Yamabe-type problems on manifolds.
Study on spinor field equation on spheres, focusing on blow-up analysis.
Paper proves a spinorial version of Aubin's estimate for the Yamabe problem.
We consider a spinorial Yamabe-type problem on open manifolds of bounded geometry. The aim is to study the existence of solutions to the associated Euler-Lagrange-equation. We show that under suitable assumptions such a solution exists. As an application, we prove that existence of a solution implies the conformal Hija…
Study on solutions to spinorial Yamabe equation on manifolds with boundary.
Paper proves existence of minimum energy solutions in 5D contact spin manifolds.
The paper finds bounds for a spinorial equation and applies it to a Bär-Hijazi-Lott invariant.
In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants are characterized through Yamabe-type equations on products of spheres with rescal…
Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the -sphere, . Via variational methods and the spinorial Weierstraß representation, we study the problem of prescribing mean curvature for the imme…
The paper solves spinorial Yamabe-type problems on spheres, with applications in geometry.
The paper constructs solutions to a critical Dirac equation on spheres.
Paper introduces new fractional Dirac operator and Q-curvature.
Let $(M,g,\si)$ be a compact Riemannian spin manifold of dimension . For any metric conformal to , we denote by the first positive eigenvalue of the Dirac operator on $(M,\tilde g,\si)$. We show that $$\inf_{\tilde{g} \in [g]} \tildeλ\Vol(M,\tilde g)^{1/n} \leq (n/2) \Vol(S^n)^{1/n}.$$ T…
We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes over the infimum inside each conformal class of the first positive Dirac eigenvalue, normalized to volume 1. This invariant is a spinorial analogue of Schoen's -constant, also known as the smooth …
Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists \cite{onish1} and we treat in detail the only new series of inclusions providing the spinorial structur…
We describe the different classes of structures in terms of spinorial equations. We relate them to the spinorial description of structures in some geometrical situations. Our approach enables us to analyze invariant structures on quasi abelian Lie algebras.
In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Lie groups equipped with left invariant metrics. As applications, we get a spinorial proof of the Fundamental Theorem for submanifolds into Lie groups, we recover previously known representations of submanifolds in $\…
Let M be a compact manifold equipped with a Riemannian metric g and a spin structure \si. We let $λ(M,[g],\si)= \inf_{\tilde{g} \in [g]} λ_1^+(\tilde{g}) Vol(M,\tilde{g})^{1/n}$ where is the smallest positive eigenvalue of the Dirac operator D in the metric . A previous result stated that …
In this paper we give a geometrically invariant spinorial representation of surfaces in four-dimensional space forms. In the Euclidean space, we obtain a representation formula which generalizes the Weierstrass representation formula of minimal surfaces. We also obtain as particular cases the spinorial characterization…
Researchers found a spinorial representation for surfaces in 3D Lorentzian spaces.
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin structure carrying a partially pure spinor field. We study various integrability conditions of the alm…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, …
Spinorial approach characterizes submanifolds in product spaces of constant curvature.
Study on convergence rate of weighted Yamabe flow.
We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.
This is a companion paper to arXiv:1207.3529 where we introduced the spinorial energy functional and studied its main properties in dimensions equal or greater than three. In this article we focus on the surface case. A salient feature here is the scale invariance of the functional which leads to a plenitude of critica…
The Yamabe flow converges to a specific function on compactified manifolds.
The fractional Yamabe problem, proposed by González-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the classical Yamabe problem and the boundary Yamabe problem to the realm of nonlocal co…
Proves product metrics are Yamabe metrics under small flat torus conditions.
Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar. We observe an interesting Hopf type m…
Study solves Yamabe problems on metric measure spaces with or without boundary.
New local method solves Yamabe problems on compact and non-compact manifolds.
Paper proves uniqueness of Type II Yamabe metrics on manifolds.
Using spinorial techniques, we prove, for a class of pseudo-hyperbolic ambient manifolds, a Heintze-Karcher type inequality. We then use this inequality to show an Alexandrov type theorem in such spaces.
We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume G-invariant metrics minimizing the total scalar curvature functional in their …
Study on complex manifolds introduces a new deformation of the Yamabe problem.
New scalars measure failure of CC metrics to solve singular Yamabe problem.
We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in to other Lorentzian space forms. We also characterize immersions of Riemannia…
Constructs singular Yamabe solutions via equivariant reduction.
Solve supercritical Yamabe problem on manifolds with non-umbilic boundary.
Researchers solve Yamabe problems for specific operators, finding both uniqueness and nonuniqueness.
New mass definition for negative cosmological constant spacetimes.
We study a particular class of open manifolds. In the category of Riemannian manifolds these are complete manifolds with cylindrical ends. We give a natural setting for the conformal geometry on such manifolds including an appropriate notion of the cylindrical Yamabe constant/invariant. This leads to a corresponding ve…
The Yamabe problem in compact closed Riemannian manifolds is concerned with finding a metric with constant scalar curvature in the conformal class of a given metric. This problem was solved by the combined work of Yamabe, Trudinger, Aubin, and Schoen. In particular, Aubin solved the case when the Riemannian manifold is…
Study finds bifurcation and local rigidity points for solutions to the Yamabe problem on Aloff-Wallach Spaces.
Refines spinorial Sobolev inequality on sphere, proving stability and new properties of Killing spinors.
In this work we determine bifurcation instants for 1-parameter families of solutions to the Yamabe problem defined on maximal flag manifolds. We also study the local rigidity points, namely, a isolated solution of the Yamabe problem.