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 on convergence rate of weighted Yamabe flow.
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.
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.
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.
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.
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.
The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem.
We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with stratified spaces furnishing the key examples. The criterion for solvability there …
The paper examines stability of Yamabe boundary problem under perturbations.
We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non homothetic solutions of the Yamabe problem. Using local rigi…
Solves Yamabe problem on compact manifolds using variational methods.
Contact Riemannian manifolds, whose complex structures are not necessarily integrable, are generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection plays the role of the Tanaka-Webster connection of a pseudohermitian manifold. Conformal transformations and the Yamabe problem are a…
New iterative method solves Yamabe problem on small domains.
We describe and partially solve a natural Yamabe-type problem on smooth metric measure spaces which interpolates between the Yamabe problem and the problem of finding minimizers for Perelman's -entropy. This problem reduces in all dimensions on Euclidean space to the characterization of the minimizers of the family …
The Yamabe invariant is linked to static potentials and eigenvalues.
New solutions found for Yamabe problem on spheres with foliations.
A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
Paper solves Gauduchon scalar curvature problem on almost Hermitian manifolds.
We give a survey of various compactness and non-compactness results for the Yamabe equation. We also discuss a conjecture of Hamilton concerning the asymptotic behavior of the parabolic Yamabe flow.
We solve the -Yamabe problem for a non locally conformally flat manifold of dimension .
In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In this paper, we generalize Aubin's theorem and we prove the Hebey--Vaugon conjec…
In this paper, we consider the Yamabe equation on a complete noncompact Riemannian manifold and find some geometric conditions on the manifold such that the Yamabe problem admits a bounded positive solution.
We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded…
We study compactness of solutions to the Yamabe problem on Riemannian manifolds which are not locally conformally flat.
Solves Yamabe problem for Sobolev-class asymptotically hyperbolic manifolds.
CR structure on S³ with non-compact solutions to CR Yamabe problem.
The paper proves estimates for solutions to nonlinear equations on manifolds with boundary.
Study combinatorial Yamabe flow on infinite triangulated surfaces.
Paper solves CR positive mass and Yamabe problems on weighted spaces.
Study on compactness and blow-up of solutions for Yamabe problems on manifolds with non-umbilic boundaries.
On a closed balanced manifold, we show that if the Chern scalar curvature is small enough in a certain Sobolev norm then a slightly modified version of the Chern-Yamabe flow~\cite{Angella:2015aa} converges to a solution of the Chern-Yamabe problem. We also prove that if the Chern scalar curvature, on closed almost-Herm…
We study the Yamabe problem on open manifolds of bounded geometry and show that under suitable assumptions there exist Yamabe metrics, i.e. conformal metrics of constant scalar curvature. For that, we use weighted Sobolev embeddings.
Solutions grow for a special type of math problem on curved spaces.
Smooth solutions found for a specific type of Yamabe problem.
Given a compact Riemannian manifold, with positive Yamabe quotient, not conformally diffeomorphic to the standard sphere, we prove a priori estimates for solutions to the Yamabe problem. We restrict ourselves to the dimensions less than or equal to 7, where the Positive Mass Theorem is known to be true. We also show th…
Study asymptotic behaviors of solutions near singular boundaries for the Yamabe problem.