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.
Coercivity condition ensures learning of interacting particle systems.
Establishes convexity and coercivity of K-energy functional for complex tori.
Paper establishes maximum principles for weakly 1-coercive operators.
New convergence guarantees for SGDA and SCO under expected co-coercivity.
Extremal Kahler metrics and Sasaki-Einstein metrics characterized via coercive energy.
Synthetic approach to pluripotential theory measures finite energy.
We extend the Palais-Smale condition to Keller's -functionals on Fréchet spaces. Using this condition together with Ekeland's variational principle, we obtain some results regarding the existence of minima. In this setting, we prove that the Palais-Smale condition for functionals bounded below implies the coerci…
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
We give a criterion for the coercivity of the Mabuchi functional for general Kähler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the existence of a Kähler-Einstein metric. We also prove the alpha invariant is a continuous function on…
The most fruitful approach to studying low energy soliton dynamics in field theories of Bogomol'nyi type is the geodesic approximation of Manton. In the case of vortices and monopoles, Stuart has obtained rigorous estimates of the errors in this approximation, and hence proved that it is valid in the low speed regime. …
Last-iterate guarantees for learning in co-coercive games under noisy feedback.
In this paper, a new approach of defining Steiner symmetrization of coercive convex functions is proposed and some fundamental properties of the new Steiner symmetrization are proved. Further, using the new Steiner symmetrization, we give a different approach to prove a functional version of the Blaschke-Santalo inequa…
Proves invariance of weighted extremal Kähler metrics under smooth blowups.
Given a smooth positive measure on a complete Hermitian manifold with Ricci curvature bounded from below, we prove a pointwise Agmon-type bound for the corresponding Bergman kernel, under rather general conditions involving the coercivity of an associated complex Laplacian on -forms. Thanks to an appropriate…
We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity should be reduced with respect to the group action. About this point we explain …
The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel results, especially on the convergence rates of the objective function values. The no…
Estimates network structure and interaction rules from multiple agent trajectories.
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a st…
The paper studies the modified J-equation on Kähler manifolds.
Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.
We give sufficient conditions for a -local diffeomorphism between Fréchet spaces to be a global one. We extend the Clarke's theory of generalized gradients to the more general setting of Fréchet spaces. As a consequence, we define the Chang Palais-Smale condition for Lipschitz functions and show that a functio…
In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients of the metric, etc. We prove that these technical assumptions admit a natural i…
Study on fractional mass for codimension-two currents, proving equi-coercivity and Γ-convergence.
This is a sequel of our paper [arXiv:1809.08425] on the Quot-scheme limit and variational properties of Donaldson's functional, which established its coercivity for slope stable holomorphic vector bundles over smooth projective varieties. Assuming that the coercivity is uniform in a certain sense, we provide a new proo…
The paper proves the existence of singular cscK metrics on smoothable varieties.
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
Study on weighted cscK metrics on Kähler varieties with singularities.
The paper learns particle swarming models from data using Gaussian processes.
We show that a projective manifold is stable if and only if the Mabuchi energy is proper on the space of algebraic metrics. We show that stability implies finite automorphism group.
Paper proves existence of weighted constant scalar curvature metrics.
Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.
In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a re…
Holomorphic vector fields and anti-canonical divisors on complex manifolds are studied.
The paper guarantees global stability for stochastic subgradient methods in nonsmooth nonconvex optimization.
We show that the coercivity of the modified Ding functional leads to the existence of a certain kind of balanced metrics and their convergence to the Kähler-Ricci soliton modulo automorphisms. In our results, we do not assume that the vanishing of the higher order modified Futaki invariants introduced by Berman-Nyström…
Extends a theorem for first-order elliptic operators on manifolds.
Inexact subgradient methods work well for semialgebraic functions with additive errors.
Proves existence of weighted-cscK metrics on Kähler manifolds.
The paper studies how noise synchronizes tokens in deep transformer models.
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-di…
New approach finds analytic interpretation of algebraic invariants for balanced metrics.
For a holomorphic vector bundle over a polarised Kähler manifold, we establish a direct link between the slope stability of and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In particular, we provide an explicit estimate which proves that Donaldso…
Upper bounds for second Robin eigenvalue on Riemannian surfaces.
We study the regularity of the solutions of second order boundary value problems on manifolds with boundary and bounded geometry. We first show that the regularity property of a given boundary value problem is equivalent to the uniform regularity of the natural family of associated boundary value …
We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies K-semistability (resp. uniformly K-stable). In particular this shows that the existen…
Improved analysis of extragradient methods for structured VIPs.
In this paper, we introduce the "coupled Ricci iteration", a dynamical system related to the Ricci operator and twisted Kähler-Einstein metrics as an approach to the study of coupled Kähler-Einstein (CKE) metrics. For negative first Chern class, we prove the smooth convergence of the iteration. For positive first Chern…
Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in Kähler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as…