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.
This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic spac…
In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.
We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, SKT and astheno-Kähler metrics. We prove that the twistor spaces of compact hyperkähler and negative quaternionic-Kähler manifolds do not admit astheno-Kähler metrics. Then w…
The equality between the balanced and the Gauduchon cones is discussed in several situations. In particular, it is shown that equality does not hold on many twistor spaces, and it holds on Moishezon manifolds. Moreover, it is proved that a SKT manifold of dimension three on which the balanced cone equals the Gauduchon …
For a certain maximal unipotent family of Abelian varieties over the punctured disc, we show that after a base change, one can complete the family over a disc such that the whole degeneration can be simultaneously balanced embedded into a projective space by the theta functions. Then we study the relationship between t…
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance la…
The paper modifies twistor spaces for Kähler surfaces and finds metrics on the modified spaces.
problem Constructing a modified twistor space for Kähler surfaces and studying its properties.
method Constructing a modification S(M) of the twistor space of a Kähler scalar flat surface M and studying its complex-geometric and metric properties.
result Complete balanced metrics are constructed on S(M) and it is shown that S(M) cannot be Kähler when M is a compact simple hyperkähler manifold.
A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the three structures, and such that the corresponding Hermitian forms are closed, th…
In \cite{D3}, Donaldson defines a dynamical system on the space of Fubini-Study metrics on a polarized compact Kähler manifold. Sano proved that if there exists a balanced metric for the polarization, then this dynamical system always converges to the balanced metric (\cite{S}). In \cite{DKLR}, Douglas, et. al., conjec…
Paper surveys balanced metrics and proves a geodesic convexity result.
problem Understanding balanced metrics and stability in algebraic geometry.
method Survey and proof of geodesic convexity result.
result Geodesically convex function on a complete Riemannian manifold admits a critical point if and only if its asymptotic slope at infinity is positive.
Let M be any compact four-dimensional PL-manifold with or without boundary (e.g. the four-dimensional sphere or ball). Consider the space T(M) of all simplicial isomorphism classes of triangulations of M endowed with the metric defined as the minimal number of bistellar transformations required to transform one o…
Let X be a smooth subvariety of CP^N. We study a flow, called balancing flow, on the space of projectively equivalent embeddings of X, which attempts to deform the given embedding into a balanced one. If L->X is an ample line bundle, considering embeddings via H^0(L^k) gives a sequence of balancing flows. We prove that…
We study Smoothed Online Convex Optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a Ω(d) lower bound on the competitive ratio of any online algorithm, where d is the dimension of the action space, we ask under what conditio…
In this paper we study the convexity properties of geodesics and balls in Outer space equipped with the Lipschitz metric. We introduce a class of geodesics called balanced folding paths and show that, for every loop α, the length of α along a balanced folding path is not larger than the maximum of its lengths at th…
New approach finds analytic interpretation of algebraic invariants for balanced metrics.
problem Finding analytic interpretation of algebraic invariants for balanced metrics.
method Using log canonical thresholds and basis divisors, the approach involves quantized Ding functionals on Bergman spaces.
result Each δ_m is the coercivity threshold of a quantized Ding functional on the m-th Bergman space, characterizing the existence of balanced metrics.
An n-dimensional strictly pseudoconvex Hartogs domain D_F can be equipped with a natural Kaehler metric g_F. In this paper we prove that if m_0g_F is balanced for a given positive integer m_0 then m_0>n and (D_F, g_F) is holomorphically isometric to an open subset of the n-dimensional complex hyperbolic space.
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…
The Bott-Chern cohomology of 6-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants introduced by Angella and Tomassini and by Schweitzer, which are related to the $\pa…
FSRM method improves treatment effect estimation from observational data.
problem Estimating treatment effects from observational data with missing counterfactual outcomes and selection bias.
method FSRM method based on deep representation learning and matching, which maps covariate space into a selective, nonlinear, and balanced representation space.
result FSRM method outperforms state-of-the-art methods in estimating treatment effects.
A well-known theorem of Wolpert shows that the Weil-Petersson symplectic form on Teichmüller space, computed on two infinitesimal twists along simple closed geodesics on a fixed hyperbolic surface, equals the sum of the cosines of the intersection angles. We define an infinitesimal deformation starting from a more gene…
By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira-Spencer's local stability theorem of Kä…