An \emph{-admissible almost complex structure} on a -dimensional symplectic manifold is a -calibrated almost complex structure admitting a nowhere vanishing -closed -form . After giving some examples we consider the moduli space of admissible almost complex structures a…
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48 results for “almost calibrated forms”
Study of geometric properties of almost calibrated forms on Kähler manifolds.
problem Understanding the geometry of almost calibrated forms on compact Kähler manifolds.
method Investigates the infinite dimensional Riemannian manifold structure, CAT(0) geodesic metric space, and geodesics of the space of almost calibrated forms.
result The space of almost calibrated forms is an infinite dimensional Riemannian manifold with non-positive sectional curvature and CAT(0) geodesic metric space.
Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping the closedness assumption on $\om$, we get an almost hermitian manifold $(M, \om, …
New tan-concavity property for Lagrangian phase operators helps in studying dHYM metrics.
problem Lack of concavity in Lagrangian phase operator for dHYM metrics.
method Introduce tangent Lagrangian phase flow (TLPF) on almost calibrated (1,1)-forms.
result TLPF exists for all positive time and converges to dHYM metrics under certain conditions.
This paper improves Reifenberg's theorem for almost calibrated sets, ensuring rectifiability with volume bounds.
problem Improving the rectifiability of sets that are close to subspaces under certain calibrations.
method Using ε-calibrations and positivity conditions, the paper shows that almost calibrated sets are rectifiable with volume bounds.
result Almost calibrated sets are rectifiable with uniform volume bounds.
In this article, we determine the seven-dimensional almost Abelian Lie algebras which admit calibrated or parallel G_2-/G_2^*-structures. Along the way, we show that certain well-established curvature restrictions for calibrated and parallel G_2-structures are not valid in the G_2^* case. In more detail, we provide the…
The shear constructionmath.DG
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented a generalization of the twist, a shear construction of rank one, which allowed …
In this paper, we derive a mean curvature estimate for eternal solutions (including translating solutions) of almost-calibrated Lagrangian mean curvature flow in complex Euclidean space. As a consequence, we show a non-existence result for eternal solutions of almost-calibrated Lagrangian mean curvature flow.
Ancient solutions of Lagrangian mean curvature flow in C^n naturally arise as Type II blow-ups. In this extended note we give structural and classification results for such ancient solutions in terms of their blow-down and, motivated by the Thomas-Yau Conjecture, focus on the almost calibrated case. In particular, we c…
We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi-calibrated 2-currents
The paper extends Liouville's theorem to calibrated geometries in various dimensions.
problem Extending Liouville's theorem to calibrated geometries in different dimensions.
method Analyzing Sobolev mappings and calibrations in calibrated geometries.
result Calibrations in certain dimensions have the Liouville property.
Variational characterization of calibrated submanifolds in different contexts.
problem Characterize calibrated submanifolds using variational principles.
method Variational approach with special variations of ambient metrics and calibrations.
result Critical points of volume functional correspond to calibrated submanifolds.
New findings show that not all area-minimizing surfaces are calibrated, even on complex manifolds.
problem Understanding when area-minimizing surfaces cannot be calibrated.
method Analyzing homology classes and metrics on manifolds to determine if area-minimizers are calibrated.
result Calibrated area-minimizers are non-generic, challenging the common assumption that they are typical.
We investigate the deformation theory of a class of generalized calibrations in Riemannian manifolds for which the tangent bundle has reduced structure group U(n), SU(n), G_2 and Spin(7). For this we use the property of the associated calibration form to be parallel with respect to a metric connection which may have no…
Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.
problem Existence of solutions to the hypercritical deformed Hermitian-Yang-Mills equation.
method Introduce coerciveness and properness of the J-functional on almost calibrated (1,1)-forms.
result Equivalence of coerciveness and properness to the existence of solutions.
We prove that tangent cones to 2-dimensional calibrated cycles are unique. Using this result we prove a rate of convergence for the mass of the blow-up of a calibrated integral 2-cycle towards the limiting density. With the same techniques, we can also prove such a rate for J-holomorphic maps between almost complex man…
Linguistic calibration improves long-form text confidence.
problem LMs hallucinate, leading to suboptimal decisions.
method Defining linguistic calibration, training framework, reinforcement learning.
result Llama 2 7B is significantly more calibrated than baselines.
Smooth calibration improves forecast reliability even with leaked information.
problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.
Ancient solutions and translators identified for Lagrangian flow.
problem Characterizing ancient solutions and translators of Lagrangian mean curvature flow.
method Analyzing almost calibrated, exact, ancient solutions with specific geometric properties.
result All ancient solutions with entropy less than 3 are special Lagrangian, planes, or translators in \(\mathbb{C}^2\).
Boosting trees can test necessary conditions for regression model calibration.
problem Testing calibration and auto-calibration in regression models.
method Using boosting trees to test calibration and auto-calibration.
result Boosting trees prove to be very powerful in testing calibration and auto-calibration in large insurance datasets.
New forms calibrate minimal graphs in arbitrary dimensions.
problem Calibrating minimal graphs in arbitrary codimension.
method Constructing closed forms from minimal graphs and estimating their comass.
result Conditions ensuring minimal graphs are calibrated and area-minimizing.
Study uses Lie group subgroups to identify special subspaces in calibrations.
problem Identifying calibrated subspaces in Lie groups.
method Utilizes the principal three-dimensional subgroup of a simple Lie group.
result Identifies certain special subspaces as calibrated for invariant forms.
Study on CKY forms on almost abelian Lie groups, proving parallelism and characterizing non-parallel cases.
problem Characterizing CKY forms on almost abelian Lie groups and proving parallelism.
method Analyzing almost abelian metric Lie algebras, proving parallelism for CKY forms, and classifying cases up to dimension 5.
result CKY forms are parallel on almost abelian Lie algebras, with exceptions for and .
The paper explores families of almost complex structures and transverse (p,p)-forms.
problem Understanding and producing families of almost p-Kähler structures.
method Producing families of almost p-Kähler structures on $\C^3$, $\C^4$, and .
result The almost complex structures cannot be locally compatible with any symplectic form for .
The paper introduces new cohomologies and studies harmonic forms on almost complex manifolds.
problem Understanding cohomologies and harmonic forms on almost complex manifolds.
method Introducing new cohomologies (Bott-Chern and Aeppli) and studying associated harmonic forms.
result Bott-Chern cohomology of 1-forms is finite-dimensional on compact manifolds and provides an invariant.
Study primitive decompositions for harmonic forms on almost Kähler manifolds.
problem Decomposing harmonic forms on almost Kähler manifolds.
method Proved primitive decompositions for Bott-Chern and Aeppli harmonic forms in specific bidegrees.
result Optimal bidegrees for primitive decompositions of harmonic forms.
Exact distribution of split conformal prediction coverage found.
problem Determining the reliability of prediction sets in batch mode.
method Analysis of exchangeable data to find universal distribution of empirical coverage.
result Exact distribution of empirical coverage is universal and determined by nominal miscoverage level and calibration sample size.
Study of presymplectic forms on almost abelian Lie algebras, determining moduli spaces and their finiteness.
problem Determining conditions for the existence of presymplectic forms on almost abelian Lie algebras.
method Analyzing the moduli space of presymplectic forms and using matrix congruence to find canonical representatives.
result The moduli space of presymplectic forms on almost abelian Lie algebras is finite and all forms are permutations of a canonical 2-form.
The paper defines new modular forms from almost complex manifolds and derives anomaly cancellation formulas.
problem Anomaly cancellation in almost complex manifolds.
method Defined a generalized elliptic genus and derived SL(2,Z) modular forms.
result Derived anomaly cancellation formulas and divisibility results for holomorphic Euler characteristic.
Validation of ML-UQ calibration statistics using simulated reference values: a sensitivity analysisstat.ML
Study validates ML-UQ calibration statistics using simulated reference values.
problem Validation of ML-UQ calibration statistics is lacking due to lack of predefined reference values.
method Proposed validation workflow using simulated reference values derived from synthetic datasets.
result Some statistics, like CC and ENCE, are overly sensitive to generative distribution choice.
Planes are the only calibrated submanifolds with flat normal bundles.
problem Characterizing submanifolds with specific geometric properties.
method Using constant-coefficient differential forms and parallel calibrations.
result Calibrated submanifolds with flat normal bundles are planes.
Study shows that dimension of Dolbeault harmonic forms is not always equal to B- on certain 4-manifolds.
problem Determining the dimension of Dolbeault harmonic (1,1)-forms on almost Hermitian 4-manifolds.
method Provided examples and proved non-equality of and for certain structures.
result Dimension of Dolbeault harmonic (1,1)-forms is not always equal to B- on almost Hermitian 4-manifolds.
Focal loss improves deep neural networks' accuracy and calibration.
problem Miscalibration in deep neural networks.
method Using focal loss and temperature scaling to improve model calibration.
result Focal loss leads to state-of-the-art calibrated models without sacrificing accuracy.
The paper connects hyperbolicity in calibrated geometry to properties of Smith immersions.
problem Hyperbolicity in calibrated manifolds and its relation to Smith immersions.
method Establishes a theorem relating hyperbolicity to the equicontinuity of Smith immersions, proving a new Schwarz lemma.
result Calibrated hyperbolicity of compact -replete manifolds is equivalent to the equicontinuity of Smith immersions.
Improved segmentation model adaptation for new domains.
problem Reduced performance of pre-trained models on new domains.
method Calculated soft-label prototypes and predicted closest to class probabilities.
result Significant performance improvements on synthetic-to-real segmentation.
New findings on hypersurfaces with specific curvature properties in space forms.
problem Characterizing hypersurfaces with almost constant curvature in space forms.
method Analyzing starshaped hypersurfaces with various curvature conditions.
result Closed starshaped hypersurfaces with almost constant mean curvature or higher order mean curvature are close to geodesic spheres.
Study -harmonic forms on almost Kähler manifolds, extending vanishing theorems.
problem Analyzing -harmonic forms on complete almost Kähler manifolds.
method Decomposing -harmonic forms into Lefschetz powers of primitive forms, extending vanishing theorems.
result Spaces of harmonic -forms on vanish unless .
The paper calculates the Chern-Ricci form for a twisted almost Kähler structure.
problem Calculating the Chern-Ricci form for a specific type of almost Kähler manifold.
method Using a twisted almost Kähler structure, the paper derives an explicit formula for the local connection 1-form and calculates the Chern-Ricci form.
result An explicit formula for the local connection 1-form and the Chern-Ricci form of a twisted almost Kähler structure are provided.
We calculate intersection forms of all 4-dimensional almost-flat manifolds
The paper classifies invariant structures on complex almost Abelian groups.
problem Investigating invariant geometric structures on almost Abelian Lie groups.
method Explicit formulas for Haar measures, modular function, and generator fields were derived.
result All invariant tensor fields have constant coefficients in the invariant frame.
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-Kähler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces of harmonic forms and cohomologies with the classical de Rham, Dolbeault, Bott-Che…
Study on almost Riemann solitons with gradient or torse-forming vector fields.
problem Characterizing almost Riemann solitons with specific vector fields.
method Using Bochner formula and properties of gradient and torse-forming vector fields.
result Explicit expressions for the soliton function under gradient and torse-forming conditions.
We give the extension formulae on almost complex manifolds and give decompositions of the extension formulae. As applications, we study -forms, the -Dolbeault cohomology group and -forms on almost complex manifolds.
Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
The study examines harmonic forms on almost Hermitian manifolds and complex surfaces.
problem Analyzing harmonic forms on almost Hermitian manifolds and complex surfaces.
method Using techniques from Bott-Chern and Aeppli numbers, the study generalizes harmonic forms from complex and symplectic manifolds to almost Hermitian manifolds.
result Bott-Chern and Aeppli numbers of compact complex surfaces depend only on the topology of the underlying manifold.
The paper extends elliptic genus and proves anomaly cancellation formulas for almost complex manifolds.
problem Anomaly cancellation formulas for almost complex manifolds.
method Extended elliptic genus, proved weak Jacobi forms, derived SL_2(Z) modular forms.
result New anomaly cancellation formulas of characteristic forms for almost complex manifolds.
We study the classification of special almost hermitian manifolds in Gray and Hervella's type classes. We prove that the exterior derivatives of the symplectic form and the complex volume form contain all the information about the intrinsic torsion of the $\SUn(n)$-structure. Furthermore, we apply the obtained results …
The paper explores various forms of calibration scores and their implications for fairness.
problem The evaluation of probabilistic predictions through calibration.
method The authors organize three grouping choices and one agglomeration of group errors, providing a framework for comparing and creating new calibration scores.
result The study demonstrates that appropriate choices of grouping can provide notions of (sub-)group or individual fairness.