New estimates for Hitchin's equations at high energy.
problem Solutions to Hitchin's self-duality equations at high energy.
method New estimates and asymptotic decoupling phenomenon.
result Generalization to arbitrary Higgs bundles.
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
48 results for “Hitchin energy”
Study of energy functional on Deligne-Hitchin moduli space sections.
problem Understanding energy functionals on sections of Deligne-Hitchin moduli space.
method Generalizes energy of equivariant harmonic maps to holomorphic sections, links to meromorphic connections, and uses Willmore energy analogy.
result Shows functional is essentially Willmore energy for certain sections, distinguishes new components from twistor lines.
Strict plurisubharmonicity of the energy on Teichmüller space associated to Hitchin representationsmath.DG
Strict plurisubharmonicity proven for Teichmüller energy on Hitchin representations.
problem Proving strict plurisubharmonicity of Teichmüller energy for Hitchin representations.
method Analyzing energy functional on Teichmüller space associated to Hitchin representations.
result Strict plurisubharmonicity of energy functional proven.
Hitchin representations yield harmonic maps with energy density ≥1.
problem Characterize harmonic maps associated with Hitchin representations.
method Study -equivariant harmonic maps from a hyperbolic surface to symmetric spaces.
result Energy density of is ≥1, with equality at one point only for specific representations.
Develops Lie-theoretic perspective on Hitchin's equations for cyclic G-Higgs bundles.
problem Analytic and geometric properties of harmonic maps.
method Lie-theoretic perspective on Hitchin's equations for cyclic G-Higgs bundles.
result Proves Dai-Li's conjecture on the monotonicity of the energy density and negative curvature conjecture for Coxeter cyclic G-Higgs bundles.
Defines loop Hodge structures and connects them to harmonic bundles.
problem Understanding harmonic bundles using Hodge theory.
method Introduces loop Hodge structures and proves their equivalence to harmonic bundles.
result Establishes equivalence between loop Hodge structures and harmonic bundles, enabling classical Hodge theory tools.
The study shows how energy density of harmonic maps dominates in -Fuchsian fibers, leading to unique minimal surfaces.
problem Understanding energy density and topological invariants in -Fuchsian fibers of Higgs bundles.
method Establishing an algebraic inequality generalizing a GIT theorem to prove energy density domination.
result Energy density of harmonic maps dominates in -Fuchsian fibers, leading to unique minimal surfaces.
Paper fills in technical details for Hitchin's self-duality equations proof.
problem Existence of solutions to Hitchin's self-duality equations.
method Reduction to minimizing energy functional, Coulomb gauge construction.
result Smooth solution constructed using unitary gauge transformation.
Energy functional on Teichmüller space is plurisubharmonic but not strictly so.
problem Characterizing points where energy functional fails to be strictly plurisubharmonic.
method Analyzing the kernel of the Levi form and relating it to Higgs bundles and Hitchin fibration.
result For generic choices, energy functional is strictly plurisubharmonic.
We construct finite energy instanton connection on which are periodic in two directions via an analogue of the Nahm transform for certain singular solutions of Hitchin's equations defined over a 2-torus.
The Haydys monopole equationmath.DG
Study of Haydys monopoles using complexified Bogomolny equations.
problem Understanding the moduli space of Haydys monopoles and their geometric properties.
method Dimensional reduction of Haydys instanton equations to three dimensions; gluing construction.
result Smooth locus of Haydys monopoles on forms a Kähler manifold containing a minimal Lagrangian submanifold.
We study Hitchin representations and maximal symplectic representations of surface groups, which can be both thought of as generalisations of Fuchsian representations. We show that the corresponding energy functionals are proper on Teichmuller space. We also prove that the mapping class group acts properly on the corre…
Study of Dirac-Witten operator on Lorentzian manifolds under dominant energy condition.
problem Detecting non-trivial homotopy groups in spaces of initial data under strict dominant energy condition.
method Use index theory and Lorentzian Hitchin's α-invariant to analyze Dirac-Witten operator.
result Kernel of Dirac-Witten operator is non-trivial only if fundamental group is virtually solvable of derived length at most 2.
The paper connects Ricci flow and harmonic spinors, proving new inequalities.
problem Understanding the behavior of harmonic spinors under Ricci flow.
method Introduced a weighted monopole equations and used Perelman's entropy.
result Ricci flow is the gradient flow of energy related to harmonic spinors.
New minimal surface theory disproves a conjecture in symmetric spaces.
problem Proving the existence of unstable minimal maps in symmetric spaces.
method Using Hitchin representations and equivariant maps, with a new index bound.
result Disproves the Labourie conjecture for with .
Uniton Bundlesmath.DG
We show that a twistor construction of Hitchin and Ward can be adapted to study unitons (harmonic spheres in a unitary group). Specifically, we show that unitons are equivalent to holomorphic bundles with extra structure over a rational ruled surface with energy given by Chern class. This equivalence allows us to confi…
Recently, Donaldson proved asymptotic stability for a polarized algebraic manifold with polarization class admitting a Kähler metric of constant scalar curvature, essentially when the linear algebraic part of is semisimple. The purpose of this paper is to give a generalization of Donaldson's result t…
Study non-orientable surfaces in gauge theories, matching fluxes with homotopy classes.
problem Understanding non-orientable surfaces in gauge theory and their electric-magnetic duality.
method Reduction of twisted N=4 gauge theory on non-orientable manifolds, matching fluxes with homotopy classes.
result Verification of mirror symmetry of branes as predicted by S-duality.
For Hitchin's generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated cycles minimise a functional occurring as D-brane ener…
Surveying Hitchin representations of Fuchsian groups.
problem Understanding representations of Fuchsian groups.
method Survey and conjectural geometric description.
result Conjectural geometric picture of an augmented Hitchin component.
In this note we address the problem of finding Abelian instantons of finite energy on the Euclidean Schwarzschild manifold. This amounts to construct self-dual L^2 harmonic 2-forms on the space. Gibbons found a non-topological L^2 harmonic form in the Taub-NUT metric, leading to Abelian instantons with continuous energ…
Surveying recent developments in Hitchin moduli space geometry.
problem Understanding the asymptotic geometry of Hitchin moduli space.
method Introduction to Hitchin moduli space and hyperkähler geometry.
result Recent developments in asymptotic geometry of Hitchin moduli space.
Hitchin representations are identified by curve spectral radii.
problem Classifying isometries of Hitchin components.
method Establishing transversality for positive quadruples of flags.
result Hitchin representations are uniquely determined by spectral radii of curves.
We study Bogomolny equations on . Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using Nahm transform, we show that periodic monop…
Defines and parametrizes -type singular fibres in symplectic and odd orthogonal Hitchin systems.
problem Characterizing and understanding singular fibres in Hitchin systems.
method Stratification by semi-abelian spectral data, study of irreducible components, global description of degenerations.
result Extension of Langlands duality to -type Hitchin fibres.
Real projective surfaces with Hitchin holonomy can be related via grafting.
problem Real projective surfaces with Hitchin holonomy.
method Defining graftable curves and constructing them in the Hitchin case.
result Real projective structures with the same Hitchin holonomy are related via multi-graftings.
The paper calculates the curvature of the Hitchin connection and its modified form.
problem Calculating the curvature of the Hitchin connection.
method Direct calculation and modification of the Hitchin connection.
result A modified Hitchin connection has curvature equal to an explicit multiple of the Weil-Petersen symplectic form.
Study shows Hitchin's metric converges to a semiflat metric on the Hitchin section.
problem Understanding the asymptotic behavior of Hitchin's metric on the Hitchin section.
method Analyzing the hyperkähler metric on moduli spaces of Higgs bundles.
result The Hitchin metric converges exponentially to a semiflat metric on the Hitchin section.
Study Liouville currents for Hitchin representations using root flows.
problem Understanding Liouville currents in Hitchin representations.
method Investigate simple root flows and Liouville currents.
result Derive a Liouville volume rigidity result and construct a Liouville pressure metric.
The paper quantizes the Hitchin system using geometric quantization.
problem Quantizing the Hitchin system using geometric methods.
method Geometric quantization of the Hitchin moduli space by modifying the Quillen metric.
result The modified Kahler form is integral and descends as a prequantum line bundle.
Study asymptotics of hyperkähler geometry on singular fibers of Hitchin moduli space.
problem Asymptotic hyperkähler geometry of -Hitchin moduli space over singular fibers.
method Extension of exponential convergence results to locally fiducial Higgs bundles and subintegrable systems.
result Hyperkähler metric converges exponentially to semi-flat metric on subintegrable systems.
Generic Hitchin representations generate dense subgroups.
problem Understanding dense subgroups in SL_n(R) representations.
method Using a theorem by Rapinchuk, Benyash-Krivetz, and Chernousov.
result Generic Hitchin representations are strongly dense.
Study Fuchsian loci in -Hitchin components of a pair of pants.
problem Understanding Fuchsian loci in -Hitchin components.
method Using Bonahon-Dreyer parametrization, explicit parametrization of Fuchsian loci of a pair of pants.
result Explicit parametrization of Fuchsian loci of a pair of pants.
Study shows rapid decay of Hitchin metric from semi-flat metric on Higgs bundles.
problem Analyzing the asymptotic behavior of the Hitchin metric on moduli spaces of Higgs bundles.
method Examined the decay rate of the difference between Hitchin and semi-flat metrics on smooth spectral curves.
result Exponential decay of the difference between Hitchin and semi-flat metrics as t approaches infinity.
Study of a basic Hitchin equation on Sasakian 3-folds, showing hyperKähler metric.
problem Understanding moduli spaces of the basic Hitchin equation on Sasakian 3-folds.
method Construction of moduli space and calculation of its dimension.
result Moduli space admits a hyperKähler metric.
The paper constructs a Hitchin connection for a broad class of Kähler structures.
problem Developing a Hitchin connection for a large class of Kähler structures.
method Generalizing previous work, the paper constructs a Hitchin connection on the space of compatible complex structures on arbitrary symplectic manifolds.
result The constructed Hitchin connection is a partial connection on the tangent space of compatible complex structures, defined in a neighborhood of natural families of complex structures.
Study pressure metrics for cusped Hitchin representations.
problem Characterize cusped Hitchin representations of Fuchsian groups.
method Develop pressure metrics associated to fundamental weights and roots.
result New pressure metrics for Hilbert length when .
Survey on -Hitchin equations and Higgs bundles from geometric perspective.
problem Understanding -Hitchin equations through Higgs bundles and complex geometry.
method Review of Higgs bundles, holomorphic vector bundles, and Hermite-Yang-Mills equations; geometric tools applied to simplify equations.
result Simplified -Hitchin equations to a set of two equations for Higgs bundles.
Exponential decay observed between two metrics on a moduli space.
problem Analyzing the difference between two metrics on a moduli space.
method Proving exponential decay along generic rays in the Hitchin moduli space.
result Exponential decay of the difference between and .
The paper studies sequences of solutions to Hitchin-Simpson equations on Kähler manifolds.
problem Behavior of sequences of solutions to Hitchin-Simpson equations on Kähler manifolds.
method Compactness result for connections and renormalized Higgs fields.
result Every harmonic 1-form can be deformed into a sequence of solutions.
Study on harmonic metrics for rank 3 Higgs bundles in Hitchin section.
problem Finding compatible harmonic metrics for rank 3 Higgs bundles in the Hitchin section.
method Defined a symmetric pairing and studied spectral curves as 2-sheeted branched coverings.
result Gave a condition for Higgs bundles on or to have compatible harmonic metrics.
We study hyperkahler metrics and hyperholomorphic connections of Hitchin's moduli spaces after Gaiotto, Moore and Neitzke. Their construction via the twistor technique produces intricate wall crossing behaviors. For certain four dimensional Hitchin's moduli spaces local models and degeneration to local models near sing…
Kobayashi-Hitchin Correspondence for Saturated Reflexive Parabolic Sheaves on Kähler manifoldsmath.DG
Study Kobayashi-Hitchin correspondence for special sheaves on Kähler manifolds.
problem Understanding the Kobayashi-Hitchin correspondence for specific sheaves.
method Using Hermitian-Yang-Mills flow on Kähler manifolds with simple normal crossing divisors.
result Established the correspondence for saturated reflexive parabolic sheaves.
This paper proves Hitchin moduli spaces are ALG gravitational instantons.
problem Proving Hitchin moduli spaces are ALG gravitational instantons.
method Computing Torelli parameters for each Hitchin moduli space corresponding to different parabolic data.
result All Hitchin moduli spaces studied are ALG- gravitational instantons.
Researchers simplified Hitchin component computation for orbifold groups.
problem Computing the dimension of Hitchin components for orbifold groups.
method Reduction to orbi-curves and application of orbifold Riemann-Roch theorem.
result Dimension of Hitchin component computation simplified.
New flows defined on Hitchin components for PGL(V).
problem Understanding dynamics on Hitchin components.
method Define and analyze new flows on Hitchin components.
result Construct a global coordinate system on the Hitchin component.
New duality found between harmonic maps and self-dual solutions.
problem Establishing a connection between harmonic maps and self-dual solutions.
method Using a signature flip and gauge theoretic approach.
result Constructed families of transgressive harmonic maps with specific properties.
Symplectic coordinates found on a Hitchin component for a hyperbolic surface.
problem Parametrizing the -Hitchin component with canonical coordinates.
method Proved global Darboux coordinates with half canonical Goldman coordinates.
result Global Darboux coordinates exist for the -Hitchin component.