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.
Locally conformally Hessian manifolds are dense in radiant ones of rank 1.
Statistical Lie algebras with constant curvature are linked to locally conformally Kähler structures.
We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in $\bC^n$. Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian manifolds with boundary that equipped locally conformal Kähler metrics, provided a …
The paper constructs discrete Hessian and divdiv complexes on triangulations and proves their cohomology isomorphic to continuous versions.
The expression (-1/u) times the Hessian of u transforms as a symmetric (0,2) tensor under projective coordinate transformations, so long as u transforms as a section of a certain line bundle. On a locally projectively flat manifold M, the section u can be regarded as a metric potential analogous to the local potential …
In this paper we investigate the nature of stationary points of functionals on the space of Riemannian metrics on a smooth compact manifold. Special cases are spectral invariants associated with Laplace or Dirac operators such as functional determinants, and the total Q-curvature. When the functional is invariant under…
Constructs homogeneous Kähler structures on tangent bundles of Hessian manifolds.
Researchers solve metric curvature equations on manifolds with boundary.
There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutions are constructed in all dimensions and solutions are classified in d…
A selfsimiar manifold is a Riemannian manifold endowed with a homothetic vector field . We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian ma…
The paper describes flat Hessian metrics on surfaces and their potentials.
The study sets limits on heat equation solutions' Hessians on curved spaces.
Study on manifolds with density using modified Hessians for curvature comparison.
Bounds on Hessian of heat equation coupled with Ricci flow.
A new method simplifies HLLE for better robustness.
We give a conformal representation for indefinite improper affine spheres which solve the Cauchy problem for their Hessian equation. As consequences, we can characterize their geodesics and obtain a generalized symmetry principle. Then, we classify the helicoidal indefinite improper affine spheres and find a new family…
New proof shows affine manifolds with parallel volume are Riemannian-flat.
Paper finds local normal forms for wavefronts in flat coordinates.
This paper proves Liouville theorems for conformally invariant fully nonlinear equations.
New averaging technique speeds up Newton method convergence.
Paper proves inequalities on Hermitian manifolds with applications to bounded solutions.
New methods optimize functions faster with less gradient accuracy needed.
Paper improves a method for fast global and local convergence in optimization.
Stochastic Variance-Reduced Cubic regularization (SVRC) algorithms have received increasing attention due to its improved gradient/Hessian complexities (i.e., number of queries to stochastic gradient/Hessian oracles) to find local minima for nonconvex finite-sum optimization. However, it is unclear whether existing SVR…
New method shows Hessian estimator from random samples converges to true Hessian on complex manifolds.
While it has not yet been proven, empirical evidence suggests that model generalization is related to local properties of the optima which can be described via the Hessian. We connect model generalization with the local property of a solution under the PAC-Bayes paradigm. In particular, we prove that model generalizati…
Curved Frobenius manifolds link to Hessian metrics in geometry.
Solves Monge-Ampère equations on compact Hessian manifolds using the Perron method.
The understanding of the dynamics of the velocity gradients in turbulent flows is critical to understanding various non-linear turbulent processes. The pressure-Hessian and the viscous-Laplacian govern the evolution of the velocity-gradients and are known to be non-local in nature. Over the years, several simplified dy…
Local constancy of index for certain gradient mappings proved.
Smooth surfaces can always be locally described by Hessians.
We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order as long as those differential estimations are sufficientl…
Study proves structure results for homogeneous spaces supporting specific equations.
We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound.
The paper derives new gradient and Hessian estimates for nonlinear parabolic equations.
Study of manifolds with flat connections and diagonal metrics leading to vanishing Euler characteristic.
We propose a sample efficient stochastic variance-reduced cubic regularization (Lite-SVRC) algorithm for finding the local minimum efficiently in nonconvex optimization. The proposed algorithm achieves a lower sample complexity of Hessian matrix computation than existing cubic regularization based methods. At the heart…
Optimizes quadratic bandits with tight Hessian-dependent sample complexity bounds.
Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.
The study explores special Ricci-Hessian equations on Kähler manifolds and identifies three types of solutions.
We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is . We obtain as a consequence a Liouville theorem for entire solutio…
We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…
New compact examples of pseudo-Kähler manifolds with essential conformal transformations found.
We will consider locally conformally balanced manifolds. We prove that a locally conformally balanced condition is not stable under a small deformation. We prove that locally conformally balanced condition is stable under any proper modification. We prove that symmetric products of the Kodaira surface can be resolve to…
For the purpose of understanding second-order scalar PDEs and their hydrodynamic integrability, we introduce G-structures that are induced on hypersurfaces of the space of symmetric matrices (interpreted as the fiber of second-order jet space) and are defined by non-degenerate scalar second-order-only (Hessian) PDEs in…
We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal Kähler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.
In this paper, we study the blow-up of a locally conformal symplectic manifold.We show that there exists a locally conformal symplectic structure on the blow-up of a locally conformal symplectic manifold along a compact induced symplectic submanifold.
We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data sets that satisfy the shear-free condition. This condition is known to be necessary in order that a spacetime development admit a regular conf…