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 proves the existence of singular cscK metrics on smoothable varieties.
New approach finds analytic interpretation of algebraic invariants for balanced metrics.
Coercivity condition ensures learning of interacting particle systems.
Establishes convexity and coercivity of K-energy functional for complex tori.
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
Paper establishes maximum principles for weakly 1-coercive operators.
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…
Extremal Kahler metrics and Sasaki-Einstein metrics characterized via coercive energy.
Proves invariance of weighted extremal Kähler metrics under smooth blowups.
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 …
New convergence guarantees for SGDA and SCO under expected co-coercivity.
Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.
Extends probabilistic approach for Kahler-Einstein metrics on Fano manifolds.
Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
This paper is about the influence of Geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, in particular by the study of entire graphs with prescribed mean curvature, we consider classes of coercive d…
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…
Synthetic approach to pluripotential theory measures finite energy.
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
New properties of weighted Hilbert transform derived, useful for imaging applications.
Study on weighted cscK metrics on Kähler varieties with singularities.
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.
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…
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.
The paper studies the modified J-equation on Kähler manifolds.
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…
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…
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…
Inexact subgradient methods work well for semialgebraic functions with additive errors.
Estimates network structure and interaction rules from multiple agent trajectories.
Proves existence of weighted-cscK metrics on Kähler manifolds.
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…
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…
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…
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…
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…
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…
New method solves root-finding problems with faster convergence.
New findings on Mabuchi energy and stability of manifolds.
Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint. This work examines the choice of the thresholding operator, and asks whether it i…
Convex functions and bodies can be approximated by smoother convex functions.