Proves K-K-W type theorems for specific types of operators.
problem Analyzes conformal perturbations of twisted Dirac operators.
method Uses Kastler-Kalau-Walze type theorems for four-dimensional manifolds.
result Establishes theorems for both with and without boundary conditions.
Study different types of G_2-structures on Lie groups.
problem Characterize and find examples of G_2-structures on Lie groups.
method Analyze invariant exact locally conformal closed G_2-structures on simply connected Lie groups.
result Complete characterization of invariant exact locally conformal closed G_2-structures on simply connected Lie groups.
We introduce the notion of a conformal pseudo-subriemannian fundamental graded Lie algebra of semisimple type. Moreover we give a classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their prolongations.
This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slovák has classified all conformally invariant differential operators on locally conformally flat manifolds. We complete his results in higher spin theory by giving explicit expressions for …
An intrinsic definition in terms of conformal capacity is proposed for the conformal type of a Carnot--Carathéodory space (parabolic or hyperbolic). Geometric criteria of conformal type are presented. They are closely related to the asymptotic geometry of the space at infinity and expressed in terms of the isoperimetri…
In this paper, we give a sharp spectral characterization of conformally compact Einstein manifolds with conformal infinity of positive Yamabe type in dimension n+1>3. More precisely, we prove that the largest real scattering pole of a conformally compact Einstein manifold (X,g) is less than $\ndemi -1$ if and only …
Nonexistence theorem for product type manifolds, proving no locally conformally flat metrics.
problem Proving nonexistence of locally conformally flat metrics on product manifolds.
method Nonexistence theorem for product type manifolds.
result 4-manifold Σ_g×Σ_h does not admit locally conformally flat metrics for g≥2 and h≥1.
The paper studies prolongations of Lie algebras associated with pseudo H-type Lie algebras.
problem Investigating prolongations of Lie algebras associated with pseudo H-type Lie algebras. method Analyzing prolongations of associated fundamental graded Lie algebra and associated conformal pseudo-subriemannian fundamental graded Lie algebra.
result The prolongation of the associated conformal pseudo-subriemannian fundamental graded Lie algebra coincides with that of the associated fundamental graded Lie algebra under certain conditions.
Study on new metrics on para-Kähler-Norden manifolds with conformal deformation.
problem Exploring geometric and harmonic properties of new metrics.
method Conformal deformation of Berger-type metric, analysis of Levi-Civita link, study of curvature varieties, and harmonic maps.
result Detailed examination of curvature varieties and harmonic maps on the manifold.
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
Study shows strict inequality for Dirac-type equation on spin manifolds, leading to existence results.
problem Investigating strict inequality for a Dirac-type equation on compact spin manifolds.
method Analyzing a generalized conformally invariant equation involving the Dirac operator with a non-linear convolution term.
result Strict inequality holds, except for round sphere conformal cases, providing existence results for a ground state.
Convexity theorem for Hamiltonian actions on conformal symplectic manifolds.
problem Establishing convexity in conformal symplectic geometry.
method Proving a convexity theorem for moment maps under Lee type actions.
result Analog of Kirwan's convexity theorem in conformal symplectic geometry.
The paper proves two theorems for modified Novikov operators under conformal perturbations.
problem Proving theorems for modified Novikov operators under conformal perturbations.
method Two Kastler-Kalau-Walze type theorems for conformal perturbations of modified Novikov Operators on 4D and 6D compact manifolds.
result Obtained two Kastler-Kalau-Walze type theorems for conformal perturbations of modified Novikov Operators.
Paper proves uniqueness of Type II Yamabe metrics on manifolds.
problem Uniqueness of Type II Yamabe metrics on compact manifolds.
method Investigates sufficient conditions for metric uniqueness and proves corresponding theorems.
result Establishes sufficient condition for a metric to be the unique Type II Yamabe metric.
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
New methods improve anomaly detection with reduced false positives.
problem Effective anomaly detection with controlled error rates.
method Leave-one-out-, bootstrap-, and cross-conformal anomaly detection methods.
result Improved anomaly detection with reduced false positives.
In this paper we describe how to define the circle packing (cp) type(either cp parabolic or cp hyperbolic) of a Riemann surface of class S, and study the relation between this type and the conformal type of the surface.
Upper bounds for Steklov eigenvalues on manifolds with boundary.
problem Investigating upper bounds for the spectrum of the Steklov-type operator on Riemannian manifolds with boundary.
method Extending the Fraser-Schoen estimate to higher Steklov eigenvalues, using relative conformal volume and isoperimetric ratio.
result Established bounds for the Steklov eigenvalues in terms of relative conformal volume and isoperimetric ratio.
We study a Fefferman-type construction based on the inclusion of Lie groups SL(n+1) into Spin(n+1,n+1). The construction associates a split-signature (n,n)-conformal spin structure to a projective structure of dimension n. We prove the existence of a canonical pure twistor spinor and a light-like co…
We study conformal actions of connected nilpotent Lie groups on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q) compact manifold M supports a conformal action of a connected nilpotent group H, then the degree of nilpotence of H is at most 2p+1, assuming p <= q; further, if this maximal degree is atta…
Study on 4D Einstein manifolds with Kähler conformal geometry.
problem Exploring 4D Poincaré-Einstein manifolds with Kähler metrics.
method Formulated a Dirichlet boundary value problem and established existence and uniqueness theory.
result Existence and uniqueness of new Poincaré-Einstein metrics.
Reviews recent work on biharmonic conformal maps and their properties.
problem Understanding biharmonic conformal maps and their properties.
method Analyzes recent research on biharmonic conformal maps, immersions, and maps between manifolds.
result Links biharmonic conformal maps to isoparametric functions and Yamabe type equations.
Researchers solve conformal Killing forms on Kaehler manifolds.
problem Classifying conformal Killing forms on compact Kaehler manifolds.
method Explicit determination of conformal Killing forms in middle degree.
result First examples of conformal Killing forms not from Hamiltonian 2-forms.
The paper proves new theorems about specific types of operator perturbations.
problem Analyzing conformal perturbations of Dirac and signature operators.
method Developed Kastler-Kalau-Walze type theorems for specific operator types.
result Established new theorems for six-dimensional manifolds with boundary.
The paper proves uniformization for specific curvature types on manifolds.
problem Uniformizing fourth order conformal curvature on Riemannian manifolds.
method Proving existence of conformal deformations for specific curvature conditions.
result Existence of conformal deformations for positive Yamabe invariant and total Q-curvature.
Study shows density of mapping classes on infinite-type surfaces using quasi-conformal maps.
problem Approximating mapping classes on infinite-type surfaces with quasi-conformal maps.
method Using hyperbolic structures and quasi-conformal homeomorphisms.
result Density of mapping classes on infinite-type surfaces can be achieved using quasi-conformal maps.
We treat a non-normal Fefferman-type construction based on an inclusion $\SL(n+1)\embed\Spin(n+1,n+1)$. The construction associates a split signature (n,n)-conformal spin structure to a projective structure of dimension n. For n≥3 the induced conformal Cartan connection is shown to be normal if and only if it…
We investigate conformality of the differential of a mapping between Riemannian manifolds if the tangent bundles are equipped with a generalized metric of Cheeger-Gromoll type.
Local gradient estimates for eigenfunctions on conformal solitons improve Liouville theorems.
problem Estimating eigenfunctions on conformal solitons.
method Proving local gradient estimates for positive eigenfunctions of L-operator. result Improved Liouville theorems for Lu=0 on conformal solitons. In this paper we use the relationship between conformal metrics on the sphere and horospherically convex hypersurfaces in the hyperbolic space for giving sufficient conditions on a conformal metric to be radial under some constrain on the eigenvalues of its Schouten tensor. Also, we study conformal metrics on the spher…
Solves a conjecture using a new formula on conformally Einstein manifolds.
problem Solving a conjecture in conformal geometry.
method Using an Obata type formula established by previous works.
result Solves Hang-Yang conjecture via an Obata-type argument.
The paper examines curvature properties of a specific magnetic spacetime metric.
problem Investigating the geometric properties of Melvin magnetic spacetime metric.
method Analyzing a Melvin type static, cylindrically symmetric spacetime metric in Weyl form, considering curvature conditions and tensor properties.
result The Melvin magnetic metric is pseudosymmetric and satisfies the Roter type condition.
We establish Liouville type theorems for degenerate conformally invariant equations.
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.
The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.
problem Characterizing and classifying manifolds with specific geometric properties.
method Analyzing warped products, contact manifolds, and semi-Riemannian manifolds.
result Characterizations and classifications of weakly conformally flat and quasi-Einstein manifolds.
Study of Dirac equation with non-local nonlinearity on spheres.
problem Conformally invariant Dirac equation with non-local nonlinearity.
method Investigation of compactness, bubbling, and energy quantization of energy functional; characterization of ground state solutions; proof of Aubin-type inequality and Brezis-Nirenberg type result.
result Existence of solutions to the conformal Einstein-Dirac problem in dimension 4.
In this article, we found a connection between Brown-York mass and the first Dirichlet Eigenvalue of a Schrödingier type operator. In particular, we proved a local positive mass type theorem for metrics conformal to the background one with suitable presumptions. As applications, we investigated compactly conformal defo…
The paper proves new theorems for Dirac operators on even-dimensional manifolds with boundary.
problem Proving theorems for Dirac operators on manifolds with boundary.
method Establishing general Kastler-Kalau-Walze type theorems for conformal perturbations of Dirac operators.
result Proof of new theorems for Dirac operators on even-dimensional manifolds with boundary.
Study of conformal logarithmic Laplacian on sphere, connecting Yamabe problems and Sobolev spaces.
problem Yamabe-type problems and Sobolev spaces on the sphere.
method Detailed spectral analysis, conformal invariance, and Hilbert space introduction.
result Established precise connection between sphere and \(\mathbb{R}^N\) logarithmic Laplacian.
Study Cheeger constant and Yamabe type for ALH manifolds.
problem Understanding the Cheeger constant and Yamabe type of ALH manifolds.
method Analyzes the Cheeger constant and Yamabe type of asymptotically locally hyperbolic manifolds with conformal compactification.
result Establishes a relationship between the Cheeger constant and the Yamabe type of the conformal infinity.
In this article we study the short-time existence of conformal Ricci flow on asymptotically hyperbolic manifolds. We also prove a local Shi's type curvature derivative estimate for conformal Ricci flow.
We obtain universal models for several types of locally conformal symplectic manifolds via pullback or reduction. The relation with recent embedding results for locally conformal Kähler manifolds is discussed.
This paper addresses the so-called conformal capacities in Rn, n≥3, through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamananmurthy-Fuglede respectively) and studying their associated iso-capacitary inequalities with connection to half-diameter, mean-width, mean-c…
Proper superminimal surfaces in hyperbolic 4-space can be approximated by conformal immersions.
problem Finding conformal superminimal surfaces in hyperbolic 4-space.
method Analysis of holomorphic Legendrian curves in the twistor space of H4. result Proper conformal superminimal immersions can be approximated by smooth ones.
There are three types of hypersurfaces in a pseudoconformal space C^n_1 of Lorentzian signature: spacelike, timelike, and lightlike. These three types of hypersurfaces are considered in parallel. Spacelike hypersurfaces are endowed with a proper conformal structure, and timelike hypersurfaces are endowed with a conform…
We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat homogeneous Ricci solitons.
We prove that the problem of constructing biharmonic conformal maps on a 4-dimensional Einstein manifold reduces to a Yamabe-type equation. This allows us to construct an infinite family of examples on the Euclidean 4-sphere. In addition, we characterize all solutions on Euclidean 4-space and show that there exists a…
The paper analyzes how conformal prediction works with contaminated reference data.
problem The impact of contamination on the validity and power of conformal prediction methods.
method The paper analyzes the impact of contamination on the validity of conformal methods and proposes a data-cleaning framework to enhance power.
result The proposed data-cleaning framework can effectively enhance power while maintaining type-I error control.