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.
Paper discusses conjectures and proves some related inequalities.
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
In this paper, we proved the Normal Scalar Curvature Conjecture and the Bottcher-Wenzel Conjecture. We also established some new pinching theorems for minimal submanifolds in spheres.
In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erdős-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system …
Study on Lin-Lu-Yau curvature and diameter of amply regular graphs.
Flat minimal tori counterexamples refute Lu's second-gap conjecture.
Lu's conjecture proven for minimal surfaces in codimension two.
Lower bound on minimum vertex degree for non-negative Lin-Lu-Yau curvature on graphs.
Combinatorial approach to -Ricci and Lin-Lu-Yau Ricci curvatures on graphs
Characterizes graphs with Lin-Lu-Yau curvature at least one and explores bone-idle graphs.
Study classifies graphs with positive curvature without quadrilaterals.
Lu conjecture proven for minimal 2-spheres and surfaces under certain conditions.
Bipartite graphs with more edges than a threshold have positive curvature.
In this paper we develope a theory of reduction for classical systems with Poisson Lie groups symmetries using the notion of momentum map introduced by Lu. The local description of Poisson manifolds and Poisson Lie groups and the properties of Lu's momentum map allow us to define a Poisson reduced space.
Unified LLY Ricci curvature defined for hypergraphs.
Study Bergman kernels on Kähler manifolds, answering Lu-Tian's question.
Paper proves edge-connectivity equals minimum degree for graphs with non-negative curvature.
Inspired by the work of G. Lu on pseudo symplectic capacities we obtain several results on the Gromov width and the Hofer--Zehnder capacity of Hermitian symmetric spaces of compact type. Our results and proofs extend those obtained by Lu for complex Grassmannians to Hermitian symmetric spaces of compact type. We also c…
In this note, we study the Koszul-Brylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on Koszul-Brylinski homolo…
Study classifies Halin graphs with positive curvature.
In this note we extend to non trivial Hamiltonian fibrations over symplectically uniruled manifolds a result of Lu's, \cite{Lu}, stating that any trivial symplectic product of two closed symplectic manifolds with one of them being symplectically uniruled verifies the Weinstein Conjecture for closed separating hypersurf…
Curvature formulas on regular graphs identified bone idle edges and graphs.
The paper connects Bergman-Calabi diastasis to Kähler metrics with constant holomorphic sectional curvature.
The study finds conditions on graph complements for positive curvature.
New research shows CPE only occurs when Bayesian posterior underfits.
Poisson actions of Poisson Lie groups have an interesting and rich geometric structure. We will generalize some of this structure to Dirac actions of Dirac Lie groups. Among other things, we extend a result of Jiang-Hua-Lu, which states that the cotangent Lie algebroid and the action algebroid for a Poisson action form…
A new method reduces communication costs in decentralized optimization.
Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let \g denote the complexification of the Lie algebra of U, \g=\u^\C. Each \u-compatible triangular decomposition \g=\n_- + \h + \n_+ determines a Poisson Lie g…
The paper introduces a new type of Ricci flow on graphs to study their curvature.
We study the Futaki invariant and the Mabuchi K-energy of a Kähler manifold using the Deligne pairing technique developed in earlier papers. We first prove a rather simple characterization of the Futaki character: The Futaki character on a Q-Fano variety is the eigenvalue of the action of on , the…
New theorem on graph curvature thresholds and uniqueness.
Study on singularities of Chern-Ricci flow on complex manifolds.
We discuss an elementary consequence of the works of (1) Brett Kotschwar and Lu Wang and (2) Ovidiu Munteanu and Jiaping Wang.
Given a manifold M with an action of a quadratic Lie algebra d, such that all stabilizer algebras are co-isotropic in d, we show that the product M\times d becomes a Courant algebroid over M. If the bilinear form on d is split, the choice of transverse Lagrangian subspaces g_1, g_2 of d defines a bivector field on M, w…
Sharp bounds on diameter and eigenvalues for amply regular graphs.
Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single da…
Solves a complex Monge-Ampère equation on compact Hermitian manifolds.
New curvature measure for graphs improves diameter and eigenvalue estimates.
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 prove that the quasi-Einstein metrics found by Lü, Page and Pope on -bundles over Fano Kähler-Einstein bases are conformally Kähler and that the Kähler class of the conformal metric is a multiple of the first Chern class. A detailed study of the lowest-dimensional example of such metrics on $\mathbb…
In this note, we prove that the $\pd$- and $\barpd$-operators introduced by Gualtieri for a generalized complex structure coincide with the $\bdees$- and $\bdel$-operators introduced by Alekseev-Xu for Evens-Lu-Weinstein modules of a Lie bialgebroid.
The study classifies graphs with specific curvature and maximum degree.
We show that the number of unique function mappings in a neural network hypothesis space is inversely proportional to , where is the number of neurons in the hidden layer .
In this paper, we discuss the Weyl problem in warped product space. We obtain the openness, non rigidity and some applications. These results together with the a priori estimates obtained by Lu imply some existence results. Meanwhile we reprove the infinitesimal rigidity in the space forms.
In this note we will prove that an dimensional graphic self-shrinker in with flat normal bundle is a linear subspace. This result is a generalization of the corresponding result of Lu Wang in codimension one case.
The global holomorphic α-invariant introduced by Tian is closely related with the study in the existence of Kahler-Einstein metric. We apply the result of Tian, Lu and Zelditch on polarized Kahler metrics to approximate plurisubharmonic functions and compute the α-invariant of toric Fano manifolds.
Global inducing points improve Bayesian neural network performance.
We show that the exponential map of the Bochner connection on the restricted holomorphic tangent bundle of a complex manifold admitting the positive-definite Bergman metric coincides with the inverse of Bergman's representative map. We also present a generalization of the Lu theorem, as an application.