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arXiv research

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.

168,695 papers · 148 categories

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0111 · Jul 200519922001200920172026
9 results for “non-CSC HCMU”
On isometric minimal immersion of a singular non-CSC extremal Ka¨\ddot{a}hler metric into 3-dimensional space formsmath.DG

Paper shows non-CSC HCMU metrics can't be isometrically immersed into 3D space forms.

problem Non-CSC HCMU metrics cannot be isometrically immersed into 3D space forms.
method Using moving frames to demonstrate the impossibility of isometric minimal immersion.
result Non-CSC HCMU metrics cannot be isometrically immersed into 3D space forms.
isometric immersionnon-CSC HCMU3D space formsmoving frames
2021-12-31abs ↗pdf ↗
Classification of non-CSC extremal Kähler metrics on K-surfaces S{α}2S^2_{\{α\}} and S{α,β}2S^2_{\{α,β\}}math.DG

Study classifies special metrics on specific surfaces.

problem Classifying extremal Kähler metrics with singularities.
method Analyzes Hessian of the Curvature of the Metric on K-surfaces.
result Identifies non-CSC HCMU metrics on S{α}2S^2_{\{α\}} and S{α,β}2S^2_{\{α,β\}}.
Kähler metricsextremal metricssingularitiesHessianRiemann surfaces
2024-07-10abs ↗pdf ↗
Counting components of moduli space of HCMU spheres via weighted treesmath.GT

Counting HCMU sphere components using weighted trees.

problem Counting components of moduli space of HCMU spheres.
method Using weighted plane trees to characterize HCMU spheres with a single integral conical angle, and an explicit counting formula is derived.
result An explicit counting formula for the components of the moduli space of HCMU spheres.
HCMU surfacesCalabi extremal Kähler metricweighted plane treesmoduli spaceintegral conical angle
2025-03-26abs ↗pdf ↗
The structure of HCMU metric in a K-Surfacemath.DG

We study the basic structure of a HCMU metric in a K-Surface with prescribed singularities. When the underlying smooth surface is S2S^2, we prove the necessary condition given in [1] for the existence of HCMU metric is also sufficient.

2005-07-19abs ↗pdf ↗
HCMU metrics with cusp singularities and conical singularitiesmath.DG

An HCMU metric is a conformal metric which has a finite number of singularities on a compact Riemann surface and satisfies the equation of the extremal Kähler metric. In this paper, we give a necessary and sufficient condition for the existence of a kind of HCMU metrics which has both cusp singularities and conical sin…

2013-02-27abs ↗pdf ↗
Extremal Kähler metrics on projectivised vector bundlesmath.DG

We prove the existence of extremal, non-csc, Kähler metrics on certain unstable projectivised vector bundles (E)→M¶(E) \to M over a cscK-manifold MM with discrete holomorphic automorphism group, in certain adiabatic Kähler classes. In particular, the vector bundles E→ME \to M under consideration are assumed to split as a …

2013-01-29abs ↗pdf ↗