New compact examples of pseudo-Kähler manifolds with essential conformal transformations found.
problem Existence of essential conformal transformations in pseudo-Riemannian manifolds.
method Construction of compact locally conformally pseudo-Kähler manifolds with essential conformal transformations.
result Found compact examples of pseudo-Kähler manifolds with essential conformal transformations that are not conformally flat.
This paper discusses a counterpart of conformal prediction for e-values, conformal e-prediction. Conformal e-prediction is conceptually simpler and had been developed in the 1990s as a precursor of conformal prediction. When conformal prediction emerged as result of replacing e-values by p-values, it seemed to have imp…
In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map. We show that every injective conformal Riemannian morphism is an injective conf…
Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.
problem Understanding local diffeomorphisms of conformal circles.
method Variations of conformal circles and pseudo-Riemannian manifolds.
result Local diffeomorphisms of conformal circles are conformal local diffeomorphisms.
Study biharmonic conformal immersions into a 3D flat space, finding new examples and classifications.
problem Characterize and classify biharmonic conformal immersions into a conformally flat 3-space.
method Characterization of totally umbilical surfaces, method to produce biharmonic immersions, classification of maps, construction of examples.
result Construct many examples of biharmonic conformal immersions, including proper immersions and isometric ones.
Conformal predictive systems are a recent modification of conformal predictors that output, in regression problems, probability distributions for labels of test observations rather than set predictions. The extra information provided by conformal predictive systems may be useful, e.g., in decision making problems. Conf…
Analyzes conformal anomaly in five dimensions, identifying new boundary conformal invariants.
problem Analyzing the conformal anomaly in five dimensions.
method Detailed analysis of boundary conformal invariants, computation of heat kernel coefficients.
result Identification of a new conformal invariant involving extrinsic curvature.
Study BGG operators on homogeneous conformal geometries.
problem Finding solutions to BGG operators on homogeneous conformal geometries.
method Invariant calculus for algebraic computations.
result Explicit solutions found for conformal Killing tensors, forms, and spinors.
New theorem proves convergence of various discrete conformal structures to conformal maps.
problem Proving convergence of discrete conformal structures to conformal maps.
method General theorem using piecewise linear discrete conformal mappings and Riemannian barycentric coordinates.
result Discrete conformal mappings converge to conformal maps under certain conditions.
Develops methods for computing conformal invariants of submanifolds.
problem Computing conformal invariants of submanifolds.
method Direct construction of extrinsic ambient space, global invariants of conformally compact minimal submanifolds, introduction of conformal submanifold scalars.
result Derives an explicit Gauss--Bonnet--Chern-type formula and proves a rigidity result.
The conformal geometry of surfaces in the conformal space Q1n is studied. We classify the space-like surfaces in Q1n with vanishing conformal form up to conformal equivalence.
Improves full conformal prediction for stochastic non-conformity measures.
problem Inability of existing conditions to guarantee full conformal prediction validity under stochastic settings.
method Introduces a new sufficient condition: Conditional Independence & Permutation Invariance in Distribution.
result Corrects the insufficient condition and provides a new sufficient condition for full conformal prediction validity.
Characterizes Kerr spacetimes using conformal methods.
problem Understanding Kerr spacetimes through conformal transformations.
method Conformally covariant characterization approach.
result Ideal characterization of Kerr spacetimes.
The paper constructs new bimetric conformal invariants using metric perturbations.
problem Developing new conformal invariants in Riemannian geometry.
method Using linear metric perturbations and conformal invariants.
result New bimetric conformal invariants on 4D manifolds are derived.
The study of conformal biharmonic maps and hypersurfaces in various spaces.
problem Understanding the properties and behavior of conformal biharmonic maps and hypersurfaces.
method Investigation of the conformal bienergy functional and its critical points, focusing on hypersurfaces in spheres and hyperbolic spaces.
result Identification and classification of conformal biharmonic hypersurfaces in spheres and hyperbolic spaces, including stability analysis.
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of …
New tensors capture intrinsic embedding data of conformal hypersurfaces.
problem Classifying hypersurface invariants in conformal manifolds.
method Constructing curvatures and conformal fundamental forms.
result Finite family of tensors captures extrinsic embedding data.
The paper defines and explores Clairaut conformal submersions in Riemannian geometry.
problem Defining and characterizing Clairaut conformal submersions.
method Analyzing necessary and sufficient conditions, deriving geometric properties, and providing examples.
result Clairaut conformal submersions have constant dilation along fibers and are harmonic.
In the complex-Riemannian framework we show that a conformal manifold containing a compact, simply-connected, null-geodesic is conformally flat. In dimension 3 we use the LeBrun correspondence, that views a conformal 3-manifold as the conformal infinity of a selfdual four-manifolds. We also find a relation between the …
Quantifies uniqueness of conformal-harmonic maps on 4-manifolds.
problem Quantifying uniqueness of conformal-harmonic maps on 4-manifolds.
method Proves a quantitative uniqueness result using convexity and second order Hardy inequality.
result Proves a version of second order Hardy inequality on manifolds.
The paper studies conformal Ricci solitons in warped product spaces.
problem Characterizing conformal Ricci solitons in warped product manifolds.
method Analyzes properties of conformal Ricci solitons in warped product spaces, proving conditions for solitons and characterizing them in terms of vector fields.
result A warped product manifold admitting a conformal Ricci soliton with a concurrent potential vector field is Ricci flat.
Study proves higher-order conformal forms don't exist in odd dimensions.
problem Proving non-existence of higher-order conformal forms in odd dimensions.
method Analyzing conformal hypersurface embeddings and differential order invariants.
result General non-existence of higher-order conformal forms in odd dimensions.
We study conformal harmonic coordinates on Riemannian manifolds. These are coordinates constructed as quotients of solutions to the conformal Laplace equation. We show their existence under general conditions. We find that conformal harmonic coordinates are a close conformal analogue of harmonic coordinates. We prove u…
Classifies 1-connected Lorentzian manifolds with essential conformal groups.
problem Classifying Lorentzian manifolds with specific conformal groups.
method Proves existence of a metric making the manifold homogeneous and plane wave.
result Completes the classification of 1-connected Lorentzian manifolds with transitive conformal groups.
New geometric variant of factorization homology for conformally flat manifolds.
problem Defining invariants of conformally flat manifolds.
method Introducing a metric-dependent geometric variant of factorization homology.
result Left Kan extensions of conformally flat d-disk algebras define invariants of conformally flat manifolds. Article addresses practical challenges in conformal prediction.
problem Challenges in determining, computing, and controlling conformal prediction regions.
method Proposes a quadratic-polynomial non-conformity measure.
result Allows circumventing three challenges in full conformal prediction framework.
Boundary distances determine conformal metrics
problem Determining conformal metrics from boundary distances
method Comparing renormalized boundary distances
result Metrics are equal if distances match
This paper is part of a series of articles on noncommutative geometry and conformal geometry. In this paper, we reformulate the local index formula in conformal geometry in such a way to take into account of the action of conformal diffeomorphisms. We also construct and compute a whole new family of geometric conformal…
We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this connection are related bijectively to solutions of the conformal Killing equatio…
The paper examines conditions for conformal Ricci solitons on generalized (κ,μ)-space forms.
problem Conditions for conformal Ricci solitons on generalized (κ,μ)-space forms. method Derivation of conditions for solitons to be shrinking, steady, or expanding in terms of conformal pressure p.
result Conditions for a Ricci semi-symmetric generalized (κ,μ)-space form to form an Einstein manifold when equipped with a conformal Ricci soliton. Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We show the existence of conformal Killing forms on nearly Kaehler and weak G_2-manifolds. Moreover, we give a…
Derives stress-energy identities in Liouville theory on compact surfaces.
problem Stress-energy tensor correlation functions on compact Riemann surfaces.
method Varying correlation functions with respect to background metric, treating different types of variations separately.
result Stress-energy correlation functions expressed as differential operators acting on primary field correlation functions.
We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…
Two novel algorithms for conformal parameterization of multiply-connected surfaces.
problem Parameterization of surfaces with holes.
method Developed efficient methods using quasi-conformal theory.
result Efficient conformal parameterization of multiply-connected surfaces.
Constructs metrics with negative curvature on specific manifold types.
problem Creating negatively curved metrics on locally conformally flat manifolds.
method Using Morse functions to construct conformal metrics.
result Successfully constructs conformal metrics with negative sectional curvature.
Study on conformal transformations of Cahen-Wallach spaces, focusing on fixed points and discontinuous groups.
problem Characterizing conformal transformations of Cahen-Wallach spaces.
method Analyzing conformal transformations of indecomposable Lorentzian symmetric spaces, focusing on fixed points and discontinuous groups.
result Essential conformal transformations of conformally curved Cahen-Wallach spaces have fixed points, and such transformations cannot centralize essential homotheties.
Proposes feature conformal prediction for broader application in semantic feature spaces.
problem Establishing valid prediction intervals in semantic feature spaces.
method Extends conformal prediction to semantic feature spaces using deep representation learning.
result Feature conformal prediction outperforms regular conformal prediction under mild assumptions.
Conformal geodesics can't spiral in Riemannian manifolds.
problem Existence of spiral conformal geodesics on Riemannian manifolds.
method Analyzing properties of conformal geodesics on Riemannian manifolds.
result No conformal geodesic can become trapped in every neighborhood of a point.
A robust conformal method for set estimation using non-conformity scores.
problem Lack of robustness in standard conformal prediction methods for outliers or heavy tails.
method Robust conformal method based on non-conformity score defined as half-mass radius.
result Empirical conformal regions converge to robust population central set.
There is a Lorenzian group acting on the conformal space Qpn. We study the regular submanifolds in the conformal space Qpn and construct general submanifold theory in the conformal space Qpn. Finally we give the first variation formula of the Willmore volume functional of subma…
By a conformal string in Euclidean space is meant a closed critical curve with non-constant conformal curvatures of the conformal arclength functional. We prove that (1) the set of conformal classes of conformal strings is in 1-1 correspondence with the rational points of the complex domain $\{q\in \mathbb{C} \,:\, 1/2…
New invariant connects boundary PDEs and conformal geometry.
problem Global conformal invariants of boundary PDEs.
method Variational considerations and conformal invariants.
result Compact Bach-flat manifolds with umbilic boundary admit Poincaré-Einstein metrics.
New tensors help determine if metrics are related to Poincaré-Einstein ones.
problem Determining when metrics on conformally compact manifolds are related to Poincaré-Einstein metrics.
method Developed new tensors and used conformal tractor calculus to analyze metrics.
result The vanishing of these new tensors is a necessary and sufficient condition for a metric to be related to a Poincaré-Einstein metric.
Classifies conformal transformations in spacetimes without observer horizons.
problem Understanding conformal transformations in spacetimes without observer horizons.
method Proves classification of conformal transformations into two types: escaping and non-escaping.
result Conformal transformations of Einstein's static universe are classified.
The paper characterizes Kenmotsu manifolds with conformal η-Ricci solitons.
problem Characterizing Kenmotsu manifolds with conformal η-Ricci solitons.
method Investigating the nature of conformal η-Ricci solitons within the framework of Kenmotsu manifolds.
result An η-Einstein Kenmotsu manifold admitting conformal η-Ricci soliton is an Einstein one.
Generalizes warped product submersion to conformal case.
problem Understanding angles preservation in submersions.
method Introduces conformal warped product submersion.
result Fundamental tensors derived for conformal submersion.
Study characterizes conformal boundaries of de Sitter spacetimes.
problem Characterize conformal infinity of asymptotically de Sitter spacetimes.
method Derive constraints relating stress-energy tensor to conformal geometric data using higher conformal fundamental forms.
result Constraints on stress-energy tensor relate to conformal geometric data.
New variational principles found for conformal geodesics.
problem Challenges in Lagrangian formulation for conformal geodesics.
method Enlarging the class of variations leads to a variational formulation with a third-order conformally invariant Lagrangian.
result Some integral curves of the fourth-order ODE system are spirals.