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 establishes boundary estimates for solutions to elliptic equations on Hermitian manifolds.
Solves Dirichlet problem for elliptic equations on Hermitian manifolds.
Proves solutions to elliptic equations on Hermitian manifolds with optimal conditions.
Sharp L∞ estimates for fully non-linear elliptic equations on compact complex manifolds.
Derives estimates for geometric elliptic equations on complex manifolds.
Study fully nonlinear elliptic equations on complex manifolds.
Paper establishes estimates for solutions on compact manifolds.
Solves Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space
Paper solves complex equations on noncompact manifolds.
Paper generalizes sub-slope definition and solves complex equations on compact manifolds.
Extends parabolic study to flat hyperkähler manifolds.
Study fully nonlinear elliptic equations on compact hyperhermitian manifolds.
Proves C^2,alpha estimates for elliptic equations on hyperkähler manifolds.
We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex Monge-Ampère, Hessian and inverse Hessian equations. As an application we solve a class of He…
Study elliptic equations on hyperhermitian manifolds with flat hyperkähler metric.
A notion of parabolic C-subsolutions is introduced for parabolic equations, extending the theory of C-subsolutions recently developed by B. Guan and more specifically G. Székelyhidi for elliptic equations. The resulting parabolic theory provides a convenient unified approach for the study of many geometric flows.
Study shows solutions to certain equations form smooth manifolds.
Uniform bounds derived for fully non-linear equations.
Study fully nonlinear equations on Hermitian manifolds to find metrics with specific curvature.
Study improves understanding of solutions to complex equations in geometry.
Solves open problems for fully nonlinear elliptic equations on manifolds.
We prove the existence of non-smooth solutions to fully nonlinear uniformly elliptic equations.
The paper examines solutions to a specific type of nonlinear equation in a disk, proving existence and uniqueness.
We prove that there is no nontrivial homogeneous order 2 solutions of fully nonlinear uniformly elliptic equations in dimension 4.
Solves a specific Dirichlet problem on Riemannian manifolds.
We prove estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. These equations are not arbitrary, but arise naturally in the study of conformal geometry.
Study shows long-term solutions for complex equations on curved spaces.
New method for analyzing elliptic and parabolic equations.
We study Hessian fully nonlinear uniformly elliptic equations and show that the second derivatives of viscosity solutions of those equations (in 12 or more dimensions) can blow up in an interior point of the domain. We prove that the optimal interior regularity of such solutions is no more than C^{1+ε}, showing the opt…
We use the octonion algebra to construct singular solutions of Hessian fully nonlinear uniformly elliptic equations in 21 or more dimensions. The regularity of these solutions is the least possible one. The same is proven for Isaacs equtions.
We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. Under the assumption of cone condition, we derive the estimate directly.
Estimates for complex equations on manifolds derived from a conjecture.
Solves nonlinear problems on metric structures through eigenvalue counting.
We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from estimates. Also, the method is flexible and can be applied to a large class of equations.
We solve the Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds under essentially optimal structure conditions, especially with no restrictions to the curvature of the underlying manifold and the second fundamental form of its boundary. The main result (Theorem 1.1) includes a new (and opt…
The paper studies fully nonlinear equations on Hermitian manifolds, proving existence and interior estimates.
We give a generalization of a theorem of Bôcher for the Laplace equation to a class of conformally invariant fully nonlinear degenerate elliptic equations. We also prove a Harnack inequality for locally Lipschitz viscosity solutions and a classification of continuous radially symmetric viscosity solutions.
We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and existence results.
In this paper we prove non-existence and classification results for elliptic fully nonlinear elliptic degenerate conformal equations on certain subdomains of the sphere with prescribed constant mean curvature along its boundary. We also consider non-degenerate equations. Such subdomains are the hemisphere (or a geodesi…
Note on advancements in nonlinear elliptic equations' regularity theory.
We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. We derive {\em a priori} estimates, and then prove the existence of admissible solutions. In the approach, a new Hermitian metic is constructed to launch the method of continuity.
This study solves a Dirichlet problem for specific elliptic equations on Riemannian manifolds with concave boundaries.
Paper studies solutions to a specific equation in conformal geometry with singular sets.
We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised by Manfredi & Mingione (Math. Ann. 2007) where only dimension dependent bounds for the growth exponent …
In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformall…
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
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 give a review of the systematic construction of hierarchies of soliton flows and integrable elliptic equations associated to a complex semi-simple Lie algebra and finite order automorphisms. For example, the non-linear Schrödinger equation, the n-wave equation, and the sigma-model are soliton flows; and the equation…