On-device research index

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.

169,341 papers · 148 categories

Trend · papers per month

count % of corpus

16 results for “T^2-cones”

Example of Compact Special Lagrangians with a Stable Singularitymath.DG

Constructs special Lagrangians with stable singularities.

problem Creating compact special Lagrangians with stable singularities.

method Constructs families of compact almost Calabi-Yau manifolds and special Lagrangians.

result Models stable T^2-cones as compact special Lagrangians.

special Lagrangians Calabi-Yau manifolds stable singularities compact manifolds T^2-cones

2016-01-09abs ↗pdf ↗

The geometric complexity of special Lagrangian

T^2

-conesmath.DG

We prove a number of results relating various measures (volume, Legendrian index, stability index, and spectral curve genus) of the geometric complexity of special Lagrangian $T^2$ -cones. We explain how these results fit into a program to understand the "most common" three-dimensional isolated singularities of special …

2003-07-09abs ↗pdf ↗

A circle quotient of a

G_2

conemath.DG

Study of a $G_2$ cone quotient with $U(1)$ action.

problem Understanding a

G_2

cone quotient with

U(1)

action.

method Analyzing the quotient space

R^6

from

R^+ imes CP^3

with

U(1)

action, finding induced metrics and curvature/symplectic forms.

result Closed expressions for the induced metric, curvature, and symplectic forms are found, invariant under

SO(3)

action.

G2 cone quotient space U(1) action holonomy metric

2019-10-21abs ↗pdf ↗

Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G_2-Laplacian Flowmath.DG

Uniqueness proven for specific types of geometric structures.

problem Proving uniqueness of asymptotically conical gradient shrinking solitons.

method Extends Kotschwar and Wang's argument for uniqueness of AC gradient shrinking Ricci solitons.

result G_2-structures are equivalent if asymptotically conical and asymptotic to the same closed G_2-cone.

G_2-structures gradient shrinking solitons Laplacian flow asymptotically conical uniqueness

2022-10-14abs ↗pdf ↗

SU(2)^2xU(1)-invariant G_2-instantons on the AC limit of the C7 familymath.DG

Constructs instantons on a specific G_2-manifold limit.

problem Finding instantons on a particular G_2-manifold limit.

method Dynamical systems approach involving perturbations of abelian and cone solutions.

result Obtains a 1-parameter family of SU(2) instantons with bounded curvature.

instantons G_2-manifolds asymptotically conical SU(2) invariance dynamical systems

2022-02-10abs ↗pdf ↗

Deformations and desingularizations of conically singular associative submanifoldsmath.DG

This study addresses transitions in conically singular associative submanifolds and their desingularizations.

problem Counting closed associative submanifolds of

G_2

-manifolds and understanding transitions arising from degenerations.

method Analysis of moduli spaces, transversality results, and desingularization techniques for conically singular associative submanifolds.

result For generic co-closed

G_2

-structures, there are no CS associative submanifolds with stability-index greater than 0 or 1.

conically singular associative submanifolds transitions desingularization G2-manifolds moduli spaces

2023-10-03abs ↗pdf ↗

Cohomogeneity-one solitons in Laplacian flow: local, smoothly-closing and steady solitonsmath.DG

Study of solitons in Laplacian flow on 7-manifolds.

problem Understanding finite-time singularities of Laplacian flow on G_2-structures.

method Systematic study of cohomogeneity-one solitons with Sp(2) and SU(3) symmetry groups.

result Existence and classification of smoothly-closing solitons, including complete and incomplete solutions.

Laplacian flow G_2-structures solitons cohomogeneity-one steady

2021-12-16abs ↗pdf ↗

M-theory on `toric' G_2 cones and its type II reductionhep-th

We analyze a class of conical G_2 metrics admitting two commuting isometries, together with a certain one-parameter family of G_2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we write down the explicit G_2 metric for the most general member of this family and extr…

2002-05-08abs ↗pdf ↗

M-theory compactifications on certain `toric' cones of

G_2

holonomyhep-th

We develop methods to study the singularities of certain $G_2$ cones related to toric hyperkahler spaces and Einstein selfdual orbifolds. This allows us to determine the low energy gauge groups of chiral N=1 compactifications of M-theory on a large family of such backgrounds, which includes the models recently studied …

2002-04-29abs ↗pdf ↗

Bryant-Salamon

\mathrm{G}_2

manifolds and coassociative fibrationsmath.DG

Constructs new coassociative fibrations for G2 manifolds.

problem Tackles the construction of new coassociative fibrations for G2 manifolds.

method Constructs fibrations by coassociative 4-folds, relates to hypersymplectic geometry and Donaldson's work.

result Shows natural generalizations of known coassociative fibrations.

G2 manifolds coassociative fibrations asymptotically conical hypersymplectic geometry Donaldson's work

2020-02-15abs ↗pdf ↗

Deformation theory of G_2 conifoldsmath.DG

We consider the deformation theory of asymptotically conical (AC) and of conically singular (CS) $G_2$ -manifolds. In the AC case, we show that if the rate of convergence $ν$ to the cone at infinity is generic in a precise sense and lies in the interval $(-4, 0)$ , then the moduli space is smooth and we compute its dimen…

2012-12-28abs ↗pdf ↗

Kurdyka-Łojasiewicz exponent via inf-projectionmath.OC

Paper shows how KL exponent is preserved via inf-projection for optimization problems.

problem Estimating the KL exponent for optimization problems.

method Shows KL exponent preservation via inf-projection for optimization problems.

result KL exponent is preserved via inf-projection for several important convex optimization models.

Kurdyka-Lojasiewicz exponent inf-projection optimization convex optimization nonconvex optimization

2019-02-10abs ↗pdf ↗

Sp(2)-invariant expanders and shrinkers in Laplacian flowmath.DG

Researchers found a family of Sp(2)-invariant solitons for Laplacian flow.

problem Analyzing Sp(2)-invariant solitons for Laplacian flow on the 4-sphere.

method Used mathematical analysis and asymptotic cone determination.

result Identified a 1-parameter family of Sp(2)-invariant expanding solitons with specific asymptotic behavior.

Laplacian flow Sp(2)-invariant solitons asymptotic cones 4-sphere

2025-01-09abs ↗pdf ↗

Ruled special Lagrangian 3-folds in C^3math.DG

This is the fourth in a series of papers math.DG/0008021, math.DG/0008155, math.DG/0010036 constructing explicit examples of special Lagrangian submanifolds (SL m-folds) in C^m. A submanifold of C^m is ruled if it is fibred by a family of real straight lines in C^m. This paper studies ruled special Lagrangian 3-folds i…

2000-12-08abs ↗pdf ↗

Infinitely many new families of complete cohomogeneity one G_2-manifolds: G_2 analogues of the Taub-NUT and Eguchi-Hanson spacesmath.DG

New G_2-manifolds with unique AC geometry discovered.

problem Finding new G_2-manifolds with specific asymptotic properties.

method Constructing 1-parameter families of G_2-manifolds with controlled geometry at infinity.

result Infinitely many new AC G_2-manifolds discovered, including unique examples.

G_2-manifolds cohomogeneity one asymptotically conical hyperKaehler Taub-NUT

2018-05-07abs ↗pdf ↗

Special Lagrangian submanifolds with isolated conical singularities. V. Survey and applicationsmath.DG

This is the last in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m with isolated sin…

2003-03-21abs ↗pdf ↗