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.
Solution to qc Yamabe problem on non-spherical quaternionic contact manifolds.
A complete solution to the quaternionic contact Yamabe equation on the qc sphere of dimension as well as on the quaternionic Heisenberg group is given. A uniqueness theorem for the qc Yamabe problem in a compact locally 3-Sasakian manifold is shown.
Conformal qc geometry of spherical qc manifolds are investigated. We construct the qc Yamabe operators on qc manifolds, which are covariant under the conformal qc transformations. A qc manifold is scalar positive, negative or vanishing if and only if its qc Yamabe invariant is positive, negative or zero, respectively. …
We report on some aspects and recent progress in certain problems in the sub-Riemannian CR and quaternionic contact (QC) geometries. The focus are the corresponding Yamabe problems on the round spheres, the Lichnerowicz-Obata first eigenvalue estimates, and the relation between these two problems. A motivation from the…
We present a gluing construction which adds, via a localized deformation, exactly Delaunay ends to generic metrics with constant positive scalar curvature. This provides time-symmetric initial data sets for the vacuum Einstein equations with positive cosmological constant with exactly Kottler-Schwarzschild-de Sitter en…
A quaternionic contact (qc) heat equation and the corresponding qc energy functional are introduced. It is shown that the qc energy functional is monotone non-increasing along the qc heat equation on a compact qc manifold provided certain positivity conditions are satisfied.
We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space $\Hnn$ and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in $\Hnn$ is contained in one of the three qc-hyperquadrics in $\Hnn$. Moreover, we show tha…
We show that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. We also show that any nowhere umbilical qc hypersurface in a hyper-Kähler manifold is endowed with an involutiv…
The paper establishes sub-gradient estimates and entropy formulas for quaternionic contact geometry heat equations.
Study on quaternionic contact structures with integrable complementary distribution.
We prove a quaternionic contact versions of the Obata's sphere theorems. We show that if the first positive eigenvalue of the sub-Laplacian on a compact qc manifold of dimension bigger than seven takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard…
In a recent paper (gr-qc/0509107) the author and Rick Schoen obtained a generalization to higher dimensions of a classical result of Hawking concerning the topology of black holes. It was proved that, apart from certain exceptional circumstances, cross sections of the event horizon, in the stationary case, and 'weakly …
QC-ST and CoCo methods correct batch effects in metabolomics data.
The paper proves new curvature estimates in quaternionic contact geometry.
The main result is that the qc-scalar curvature of a seven dimensional quaternionic contact Einstein manifold is a constant. In addition, we characterize qc-Einstein structures with certain flat vertical connection and develop their local structure equations. Finally, regular qc-Ricci flat structures are shown to fibre…
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been developed and has made significant contributions to medical imaging, computer graphics and computer vision. Existing computational QC theor…
Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…
The 'anholonomic frame' method (see gr-qc/0005025, gr-qc/0001060 and hep-th/0110250) is applied for constructing new classes of exact solutions of vacuum Einstein equations with off-diagonal metrics in 4D and 5D gravity. We examine several black tori solutions generated by anholonomic transforms with non-trivial topolo…
In this note, we prove that the CR manifold which is induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by O. Biquard.
We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of Carnot-Carathéodory metric in the conformal class. The result of this computation has appli…
We investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)H^*, and show that any qc structure gives rise to a canonical K-structure with constant intrinsic torsion, except in se…
New knots not rationally concordant to their reverses found.
Quaternion Conformer GAN (QC-GAN) is a parameter-efficient speech enhancement framework that combines a Quaternion Conformer generator with MetricGAN-based training.
Quantum computing improves fault diagnosis in industrial processes.
This paper analyzes convergence of DP-SGD with adaptive quantile clipping.
Unified AI system for data quality control and governance in regulated environments.
Study on convergence rate of weighted Yamabe flow.
Hybrid QC system for Bengali questions using smart data balancing.
Study bifurcations and local rigidity on flag manifolds for Yamabe solutions.
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.
The paper solves the Yamabe problem on certain noncompact manifolds.
Flow proposed to solve Chern-Yamabe problem, showing it's an Euler-Lagrange equation of a functional.
Generalizes Aubin's result for Yamabe-type problem on smooth metric measure spaces.
The Chern-Yamabe flow solves curvature problems on specific 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.
Solutions blow up for Yamabe problem on umbilic manifolds with nonzero Weyl tensor.
A novel density-based approach QC detects outliers in data with high precision.
On 7D quaternionic contact manifolds, eigenvalue bounds imply special structure.
Constructs singular Yamabe solutions via equivariant reduction.
Solve supercritical Yamabe problem on manifolds with non-umbilic boundary.