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.
Blowups of Kähler manifolds can inherit extremal metrics.
New extremal metrics found on Kähler manifolds.
Paper explores new Kähler metrics from old, aiming to solve YTD conjecture.
Extremal metrics exist if uniformly -stable over models.
The study finds no extremal metrics for eigenvalues on compact manifolds but constructs examples for annuli.
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
Uniqueness of weighted extremal metrics on Kähler manifolds proven.
The paper classifies rotationally symmetric extremal Kähler metrics on complex manifolds.
We give a moment map interpretation of some relatively balanced metrics. As an application, we extend a result of S. K. Donaldson on constant scalar curvature Kähler metrics to the case of extremal metrics. Namely, we show that a given extremal metric is the limit of some specific relatively balanced metrics. As a coro…
We provide a new proof of a result of X.X.Chen and G.Tian : for a polarized extremal Kähler manifold, an extremal metric attains the minimum of the modified K-energy. The proof uses an idea of C.Li adapted to the extremal metrics using some weighted balanced metrics.
Unique extremal Kähler metric found near a divisor.
Non-convex extremal length found in surface metrics.
We prove that the existence of extremal metrics implies asymptotically relative Chow stability. An application of this is the uniqueness, up to automorphisms, of extremal metrics in any polarization.
Study confirms conjecture on extremal length of hyperbolic metrics.
New toric Fano manifolds found without extremal Kähler metrics.
This paper is a survey of some recent progress on the study of Calabi's extremal Kähler metrics. We first discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion and we give some example settings where this conjecture has been established. We then tu…
Three distinct 3D components found in local extremal Kähler metrics.
We study algebro-geometric consequences of the quantised extremal Kähler metrics, introduced in the previous work of the author. We prove that the existence of quantised extremal metrics implies weak relative Chow polystability. As a consequence, we obtain asymptotic weak relative Chow polystability and -semistabili…
In this paper, we consider a compact Kahler manifold with extremal Kahler metric and a Mumford stable holomorphic bundle over it. We proved that, if the holomorphic vector field defining the extremal Kahler metric is liftable to the bundle and if the bundle is relatively stable with respect to the action of automorphis…
Investigates conditions for non-rigidity in extremal metrics involving scalar curvature.
Explain convexity of K-energy leading to unique metrics.
Bi-invariant metrics on Lie groups and homogeneous spaces are extremal and rigid.
We prove a theorem which asserts that the Lie algebra of all holomorphic vector fields on a compact Kähler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal Kähler metric proved by Calabi.
In this paper we extend recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of constant scalar Kähler metric on a compact Kähler manifold to Calabi's extremal metric. Our argument follows \cite{CC3} and there are no new a prior estimates needed, but rather there are necessary modifications adapted to th…
Fano varieties get Mabuchi solitons if they have extremal Kähler metrics.
El Soufi-Ilias' theorem establishes a connection between minimal submanifolds of spheres and extremal metrics for eigenvalues of the Laplace-Beltrami operator. Recently, this connection was used to provide several explicit examples of extremal metrics. We investigate the maximality of these metrics and prove that all o…
We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relati…
The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show that these two problems are in fact intimately related. Extremal Kahler metrics are…
Consider a compact Kähler manifold X with a simple normal crossing divisor D, and define Poincaré type metrics on X\D as Kähler metrics on X\D with cusp singularities along D. We prove that the existence of a constant scalar curvature (resp. an extremal) Poincaré type Kähler metric on X\D implies the existence of a con…
Study classifies special metrics on specific surfaces.
Blowups of Kähler manifolds with extremal metrics inherit such metrics under stability conditions.
Based on recent work of S. K. Donaldson and T. Mabuchi, we prove that any extremal Kaehler metric in the sense of E. Calabi, defined on the product of polarized compact complex projective manifolds is the product of extremal Kaehler metrics on each factor, provided that the integral Futaki invariants of the polarized m…
Sharp inequalities and extremizers for J functional on Kähler manifolds.
We apply recently developed convex programs to find the minimal-area Riemannian metric on -sided polygons () with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with the conformal extremal metric on the regular -gon. The hexagon was considered…
We generalize the bifurcation technique of Bando-Mabuchi in the context of extremal metrics.
Consider a fibred compact Kähler manifold X endowed with a relatively ample line bundle, such that each fibre admits a constant scalar curvature Kähler metric and has discrete automorphism group. Assuming the base of the fibration admits a twisted extremal metric where the twisting form is a certain Weil-Petersson type…
The paper explores existence and non-existence of constant scalar curvature and extremal Sasaki metrics.
We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain perturbed harmonic maps with constant density.
We give conditions under which the blowup of an extremal Kähler manifold along a submanifold of codimension greater than two admits an extremal metric. This generalizes work of Arezzo-Pacard-Singer, who considered blowups in points.
In this paper, we discuss a Donaldson's version of the modified -energy associated to the Calabi's extremal metrics on toric manifolds and prove the existence of the weak solution for extremal metrics in the sense of convex functions which minimizes the modified -energy.
The first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called extremal metrics. The only known extremal metrics are a round sphere, a standard projective plane, a Clifford torus and an equilateral torus.…
Let (X,L) be a polarized Kähler manifold that admits an extremal Kähler metric in c1(L). We show that on a nearby polarized deformation that preserves the symmetry induced by the extremal vector field of (X,L), the modified K-energy is bounded from below. This generalizes a result of Chen, Székelyhidi and Tosatti to ex…
Extremal metrics lead to scalar-flat Kähler cones.
The paper proves the existence of a special Kähler metric on a minimal ruled surface.
The aim of this article is to study expansions of solutions to an extremal metric type equation on the blow-up of constant scalar curvature Kähler surfaces. This is related to finding constant scalar curvature Kähler (cscK) metrics on K-stable blow-ups of extremal Kähler surfaces
New examples show Sasaki manifolds without extremal metrics.
In this paper we give sufficient conditions on a compact orbifold with an extremal Kaehler metric to admit a resolution with an extremal Kaehler metric. We also complete the Kaehler constant scalar curvature case.
Continuity method proves existence of Mabuchi solitons on Fano manifolds.