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.
New estimate for complex Monge-Ampère equations improves previous results.
Gradient estimate proved for Donaldson's equation on Kähler manifolds.
Sharp ABP estimate on metric spaces via optimal transport.
Deep Reinforcement Learning (RL) is proven powerful for decision making in simulated environments. However, training deep RL model is challenging in real world applications such as production-scale health-care or recommender systems because of the expensiveness of interaction and limitation of budget at deployment. One…
Proves inequalities for tensor fields on submanifolds using ABP method.
Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.
Employing a notion of curvature for arbitrary closed sets we prove an ABP-type estimate for a class of singular submanifolds of arbitrary codimension and bounded mean curvature recently introduced by B. White. A weak-Harnack-type estimate is then derived using the ABP estimate. These results generalize analogous result…
Develop an ABP approach to Sobolev and Michael-Simon inequalities beyond Euclidean volume growth.
The ABP method is used to prove geometric inequalities for submanifolds and tensors.
New Sobolev inequalities found for curved spaces.
New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.
Sharp inequalities for manifolds with nonnegative curvature.
Machine learning predicts phase behavior in active matter suspensions.
The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.
Establishes a boundary maximum principle for varifolds with fixed contact angle.
Note establishes a local maximum principle for Ricci flow under curvature conditions.
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving …
Study proves Maximum Principles for unbounded Riemannian domains.
In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the constant in the a priori estimate of this maximum principle. In particular, this maximum principle can be applied to manifolds with Ricci curv…
Proves a principle for one-phase Bernoulli problem minimizers.
In this paper we characterize the degenerate elliptic equations F(D^2u)=0 whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum principle. We introduce an easily computed function f(t) for t > 0, determined by F, and we show that the strong maximum principle holds depending on whether the integral …
Study on maximum principles for nonlinear equations on Riemannian manifolds.
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …
In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity v…
This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like a heat equation on graphs, but it can be shown to not satisfy the maximum principle. The notion of a parabolic-like operato…
New insights into binary perceptron reveal phase transitions and algorithmic thresholds.
New principle for harmonic maps helps study higher-dimensional submanifolds.
Study compares nodal sets of solutions to the Allen-Cahn equation.
Based on works by Hopf, Weinberger, Hamilton and Evans, we state and prove the strong elliptic maximum principle for smooth sections in vector bundles over Riemannian manifolds and give some applications in Differential Geometry. Moreover, we use this maximum principle to obtain various rigidity theorems and Bernstein …
Based on ideas of L. Alías, D. Impera and M. Rigoli developed in "Hypersurfaces of constant higher order mean curvature in warped products", we develope a fairly general weak/Omori-Yau maximum principle for trace operators. We apply this version of maximum principle to generalize several higher order mean curvature est…
We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary regularity property of the smooth subsolutions along this boundary…
In this work we extend the ODE Maximum principle of Hamilton to non-compact hypersurfaces using the Omari-Yau maximum principle at infinity. As an application of this result, we investigate Inverse Mean Curvature Flow (IMCF) of non-compact hypersurfaces in hyperbolic space. Specifically, we look at bounded graphs over …
We consider geometric flow equations for contracting and expanding normal velocities, including powers of the Gauss curvature, of the mean curvature, and of the norm of the second fundamental form, and ask whether - after appropriate rescaling - closed strictly convex surfaces converge to spheres. To prove this, many a…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entro…
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all these problems. A high order maximum principle (Krener, 1977) must be used in o…
We establish a boundary maximum principle for free boundary minimal submanifolds in a Riemannian manifold with boundary, in any dimension and codimension. Our result holds more generally in the context of varifolds.
We study the strong maximum principle for horizontal (p-) mean curvature operator and p-(sub)laplacian operator on subriemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type condition on vector fields, we show the strong maximum principle holds in higher…
MEP-Net uses MEP to generate solutions from limited data.
Paper develops MRCs for supervised classification using generalized maximum entropy.
We discuss the maximum modulus principle, and weak unique continuation, for CR functions on an abstract almost CR manifold M. We investigate these matters under the assumption of weak pseudoconcavity, and obtain sharp results about propagation along Sussmann leaves.
This note is meant to introduce the reader to a duality principle for nonlinear equations that recently appeared in the literature. Motivations come from the desire to give a unifying potential-theoretic framework for various maximum principles at infinity appearing in the literature (Ekeland, Omori-Yau, Pigola-Rigoli-…
In this short note we extend Chow and Lu's advanced maximum principles for parabolic systems on closed manifolds to the case of compact manifolds with boundary, which also generalizes a Hopf type theorem of Pulemotov.
We derive a parabolic version of Omori-Yau maximum principle for a proper mean curvature flow when the ambient space has lower bound on -sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in euclidean spaces with uniform bounded second fundamenta…
Study maximal hypersurfaces in open spacetimes using a maximum principle.
We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the optimal solutions, from which the classical Pontryagin Maximum Principle is derived i…
We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of . Our result applies to…
Sharp inequality outside ball proved using Neumann method.