Calibrated geometries

1982/01/01 by Reese Harvey, H. Blaine Lawson · 1,710 citations
Engineering · Mathematics · #3D Shape Modeling and Analysis #Mathematics #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.1007/bf02392726

published in Acta Mathematica 148(0), 47-157 (Mittag-Leffler Institute)

openalex publication_date 1982/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Cited by

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• The angle criterion
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• Holographic two-point functions of heavy operators revisited
• Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in Cm
• Sphere theorems for Lagrangian and Legendrian submanifolds
• The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures with Torsion
• Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models
• A Bernstein type result for special Lagrangian submanifolds
• Exact solutions to quantum spectral curves by topological string theory
• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
• Intersection theory of coassociative submanifolds in G_(2)-manifolds and Seiberg-Witten invariants
• Brane Theory Solitons
• Characteristic Classes on Grassmann Manifolds
• Some counterexamples for the special lagrangian curvature equation
• Bernstein Type Results for Lagrangian Graphs with Partially Harmonic Gauss Map
• Relative Liouville Rigidity for Lagrangian Self-Similar Submanifolds with Legendrian Boundary
• Calabi-Yau threefolds of type K (II): Mirror symmetry
• On the Global Structure of Some Natural Fibrations of Joyce Manifolds
• Geometric invariants and the Monge-Ampere equation in Kähler geometry
• Detect duality obstruction of calibrations in smooth category
• Simultaneous desingularizations of Calabi-Yau and special Lagrangian 3-folds with conical singularities
• Bernstein Type Theorems For Minimal Lagrangian Graphs of Quaternion Euclidean space
• The Critical LYZ equation in Kähler Geometry
• Some remarks about Cauchy integrals
• Doubling Argument of the Hessian Estimate for the Special Lagrangian Equation on General Phases with Constraints
• Geometry of isoparametric hypersurfaces in Riemannian manifolds
• Minimal Lagrangian tori in Kahler Einstein manifolds
• Parabolic nef currents on hyperkaehler manifolds
• Generalized special Lagrangian fibration for Calabi-Yau hypersurfaces in toric varieties III: The smooth fibres
• Pseudo-Riemannian geometry calibrates optimal transportation
• Superconformal Quantum Mechanics from M2-branes
• Weighted Hamiltonian stationary Lagrangian submanifolds and generalized Lagrangian mean curvature flows in toric almost Calabi-Yau manifolds
• A class of fully nonlinear equations on Riemannian manifolds with negative curvature
• A Uniqueness Theorem for Gluing Special Lagrangian Submanifolds
• The real Fourier-Mukai transform of Cayley cycles
• Special Lagrangians with multiple isolated singularities
• A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations
• On the Neumann problem for the degenerate mixed equations arising in conformal geometry
• Coassociative cones that are ruled by 2-planes
• Hamiltonian stationary cones and self-similar solutions in higher dimension
• A singular profile for the relativistic heat cost and the special Lagrangian curvature equation
• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• On the exterior Dirichlet problem for Hessian quotient equations
• The second type singularity of symplectic and Lagrangian mean curvature flows
• Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials
• On the existence of geodesic connecting Lagrangian graphs in ℂⁿ
• Gluing and deformations of asymptotically cylindrical special Lagrangians
• Calibrated Manifolds and Gauge Theory
• Constructing entire minimal graphs by evolving planes
• Doubling and the two-dimensional critical valued Lagrangian phase
• Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs
• Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase
• Subspaces of Multisymplectic Vector Spaces
• Some configuration results for area-minimizing cones
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• Nodal resolution of quasiregular curves via bubble trees
• Mirror Symmetry via 3-tori for a class of Calabi-Yau Threefolds
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• Note on equivalences for degenerations of Calabi-Yau manifolds
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• Les Houches Lectures on Fields, Strings and Duality
• Intersecting D-brane Models
• Complete minimal submanifolds with nullity in Euclidean space
• Deformations in G₂ Manifolds
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• The Almost Complex Structure on \mathbb S⁶ and Related Schrodinger Flows
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• On weakly reflective submanifolds in compact isotropy irreducible Riemannian homogeneous spaces
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• From tropical curves to special Lagrangians
• Entire conformal curves are affine or have super-Euclidean energy growth
• Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4
• An introduction to conifold transitions
• Nearly Parallel G₂-Structures with Torus Symmetry
• Dirichlet problem for Krylov type equation in conformal geometry
• The Hasse Principle for Geometric Variational Problems: An Illustration via Area-minimizing Submanifolds
• Special Lagrangian Fibrations II: Geometry
• Counting Associatives in Compact G₂ Orbifolds
• Stability and the deformed Hermitian-Yang-Mills equation
• Minimal Surfaces in G2 Manifolds
• Calibrated submanifolds with flat normal bundles
• Geometry of generalized higher order fields and applications to classical linear electrodynamics
• Compact special Legendrian surfaces in S⁵
• The classical Neumann problem for a class of mixed Hessian equations
• SU(3)-structures and Special Lagrangian Geometries
• Thin instantons in G₂-manifolds and Seiberg-Witten invariants
• Hyperbolicity and Schwarz Lemmas in Calibrated Geometry
• Some results on calibrated submanifolds in Euclidean space of cohomogeneity one and two
• On tamed almost complex four manifolds
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• Exterior differential systems: a geometric approach to PDE. Lecture notes from the 1997 Daewoo workshop
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• Phenomenology from the Landscape of String Vacua
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• Generators for Rational Loop Groups and Geometric Applications
• Austere and arid properties for PF submanifolds in Hilbert spaces
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• Geodesics of positive Lagrangians from special Lagrangians with boundary
• An ansatz for constructing explicit solutions of Hessian equations
• Generalized geometry lectures on type II backgrounds
• Deformations of Asymptotically Conical Special Lagrangian Submanifolds
• Instantons in G2 manifolds from J-holomorphic curves in coassociative submanifolds
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• Special Lagrangian conifolds, I: Moduli spaces (extended version)
• Equivariant Gluing Constructions of Contact Stationary Legendrian Submanifolds of the (2n+1)-Sphere
• On the volume of a unit vector field in 3 dimensions via calibrations
• Geometric structures on G2 and Spin(7)-manifolds
• Self-shrinkers of the mean curvature flow in arbitrary codimension
• Examples of austere orbits of the isotropy representations for semisimple pseudo-Riemannian symmetric spaces
• Compact symmetric triads and symmetric triads with multiplicities
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• Deformations of minimal Lagrangian submanifolds with boundary
• On the Kaehler angles of submanifolds
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• Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space
• New examples of compact special Lagrangian submanifolds embedded in hyper-Kähler manifolds
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• SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family
• Mirror Duality via G₂ and Spin(7) Manifolds
• Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold
• Exterior differential systems and billiards
• Matchings in metric spaces, the dual problem and calibrations modulo 2
• Moduli spaces of special Lagrangians and Kähler-Einstein structures
• Singularities of symplectic and Lagrangian mean curvature flows
• Construction of exceptional Lie algebra G2 and non-associative algebras using Clifford algebra
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• A short survey on δ-ideal CR submanifolds
• M-theory branes and their interactions
• Riemannian Submanifolds
• Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flows
• Radial solutions of a fourth order Hamiltonian stationary equation
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5
• On the Moyal deformation of Nahm equations in seven dimensions
• Topological BPS charges in 10- and 11-dimensional supergravity
• M theory and singularities of exceptional holonomy manifolds
• Calibrated Subbundles in Noncompact Manifolds of Special Holonomy
• D-branes on AdS flux compactifications
• The uniqueness of tangent cones for Yang-Mills connections with isolated singularities
• Positive Self Dual Einstein Orbifolds with One-Dimensional Isometry Group
• EVOLUTION OF THE D3-BRANE FOR DYNAMICAL EMBEDDINGS
• Calabi-Yau components in general type hypersurfaces
• A survey of Calabi-Yau manifolds
• An intrinsic characterization of Kähler manifolds
• On minimal Lagrangian surfaces in the product of Riemannian two manifolds
• Exact Results for Topological Strings on Resolved Y p,q Singularities
• T4 fibrations over Calabi–Yau two-folds and non-Kähler manifolds in string theory
• Curvature of the space of positive Lagrangians
• Review of geometry and analysis
• Metrics with Exceptional Holonomy
• Mirror symmetry is T-duality
• Large Complex Structure Limits of K3 Surfaces
• Perspectives on geometric analysis
• Introduction to Smooth Manifolds
• A Morse-Bott unification of the Grassmannians of a symplectic vector space
• New invariants ofG2–structures
• Quaternion-Kahler geometry of time reversal symmetric crystals
• A construction of G₂-manifolds from K3 surfaces with a ℤ²₂-action
• Open Topological Strings and Integrable Hierarchies: Remodeling the A-Model
• Calibrations, monopoles, and fuzzy funnels
• Regularity for Hamiltonian stationary equations in ℝ_{n≤ 4}ⁿ
• Sigma-model soliton intersections from exceptional calibrations
• On Hopf hypersurfaces of the complex quadric with constant principal curvatures
• Pseudo holomorphic curves in symplectic manifolds
• Conifold transitions and five-brane condensation in M-theory onSpin(7) manifolds
• Calibrations and T–Duality
• That's a wrap!
• Yukawa couplings in intersecting D-brane models
• Seiberg-Witten type monopole equations on 8-manifolds with Spin(7) holonomy as minimizers of a quadratic action
• Stable D-branes, calibrations and generalized Calabi-Yau geometry
• Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)
• Toward de Sitter space from ten dimensions
• Introduction to \mathrm G₂ Geometry
• On G_{\mathbf 2}-Structures, Special Metrics and Related Flows
• Some remarks about Cauchy integrals and totally real surfaces in C^m
• Heinz mean curvature estimates in warped product spaces M× _e^ψ N M × e ψ N
• Desingularization of G2 manifolds with isolated conical singularities
• On the exterior Dirichlet problem for special Lagrangian equations
• DWSB in heterotic flux compactifications
• Symmetries of Lagrangian fibrations
• The classification of holomorphic (m, n)-subharmonic morphisms
• Higher-dimensional analogues of Donaldson-Witten theory
• Simplicial approximation and complexity growth
• Lectures on special Lagrangian geometry
• A boundary value problem for minimal Lagrangian graphs
• D-branes and synthetic/C^∞-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifolds
• Spectral convergence in geometric quantization on K3 surfaces
• Collapsing of Calabi-Yau manifolds and special lagrangian submanifolds
• SU(3)-structures on submanifolds of aSpin(7)-manifold
• Calibrated entanglement entropy
• Basics of M‐theory
• On different notions of calibrations for minimal partitions and minimal networks in ℝ2
• Special Bohr - Sommerfeld geometry
• E7, Wirtinger inequalities, Cayley 4-form, and homotopy
• On cohomogeneity one hyperpolar actions related to G₂
• Geodesics of Positive Lagrangians in Milnor Fibers
• OpenG2strings
• Singularities of Lagrangian mean curvature flow: zero-Maslov class case
• Pogorelov type C² estimates for sum Hessian equations
• Neumann Problems for Elliptic and Parabolic Sum Hessian Equations
• Brane Effective Actions, Kappa-Symmetry and Applications. [europepmc]
• The Geometry of m -Hyperconvex Domains. [europepmc]