Paper shows non-existence of solutions for minimal surface problems.
problem Non-existence of solutions to Dirichlet problems for minimal surfaces.
method Analyzes minimal graphs of codimension ≥2 over domains with possibly non- C 1 C^1 C 1 boundaries. result Proves non-existence of solutions in various scenarios.
Paper proves non-existence of certain convex functions on a Riemannian manifold with a pole.
problem Proving non-existence of specific convex functions on a Riemannian manifold with a pole.
method Developed notions of odd and even functions on a Riemannian manifold with a pole, proved non-existence of non-trivial and non-negative convex functions.
result Deduced non-existence of non-trivial and non-negative differentiable odd convex functions whose gradient is complete.
Paper finds a non-existence theorem for certain translators in high dimensions.
problem Non-existence of certain translators in high-dimensional spaces.
method Developed a non-existence theorem and found an example of a translator.
result Non-existence of entire Q n − 1 Q_{n-1} Q n − 1 -translators in R n + 1 \mathbb{R}^{n+1} R n + 1 . Study finds both existence and non-existence of maps in Morse boundaries.
problem Existence and non-existence of Cannon-Thurston maps in Morse boundaries.
method Examined Morse boundaries for normal subgroups.
result Found both existence and non-existence of Cannon-Thurston maps.
The study proves non-existence of Cannon-Thurston maps for certain groups.
problem Proving the non-existence of Cannon-Thurston maps for specific groups.
method Analyzing hierarchically hyperbolic groups and their boundaries.
result Non-existence of Cannon-Thurston maps for hyperbolic normal subgroups of hierarchically hyperbolic groups.
Paper shows no eternal solutions for certain flows.
problem Existence of eternal solutions for Lagrangian mean curvature flow.
method Derived mean curvature estimate for eternal solutions.
result Non-existence of eternal solutions for almost-calibrated Lagrangian mean curvature flow.
We prove some results of non-existence for solutions of the minimal surfaces equation on domain that are asymptoticaly equal to an angular sector.
Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.
problem Existence and non-existence of positive solutions for the Lane-Emden equation on Riemannian models.
method Analysis of the subcritical Lane-Emden equation on various Riemannian manifolds with polynomial volume growth.
result Subcritical regime divides into three ranges with distinct existence and non-existence phenomena.
New results on non-existence and rigidity of spacelike submanifolds in spacetimes.
problem Non-existence and rigidity of spacelike submanifolds with causal mean curvature vector field.
method General results for various spacetimes including globally hyperbolic, stationary, and pp-wave spacetimes.
result Significant consequences in Geometrical Analysis, solving new Calabi-Bernstein and Dirichlet problems.
This paper establishes geometric obstructions to the existence of complete, properly embedded, mean curvature flow self-translating solitons Σ n ⊆ R n + 1 Σ^n\subseteq \mathbb{R}^{n+1} Σ n ⊆ R n + 1 , generalizing previously known non-existence conditions such as cylindrical boundedness.
Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.
problem Finding unique and non-existent constant mean curvature spacelike hypersurfaces.
method Geometric and physical assumptions applied to Generalized Robertson-Walker spacetimes.
result New uniqueness and non-existence results for complete spacelike hypersurfaces.
Paper proves non-existence of certain hypersurfaces in complex quadric.
problem Non-existence of Hopf real hypersurfaces with parallel normal Jacobi operator.
method Introducing C \mathcal C C -parallel and Reeb parallel normal Jacobi operators, proving non-existence theorems. result Non-existence of Hopf real hypersurfaces with C \mathcal C C -parallel normal Jacobi operator. Paper disproves existence of complex structure on 6-sphere.
problem Existence of complex structure on 6-sphere.
method Uses ideas from 50 years ago, clarified notation.
result Proves non-existence of complex structure on 6-sphere.
New technique clusters and classifies datasets with missing attributes.
problem Clustering and classification issues with incomplete data.
method Modified K-MEANS++, Scalable K-MEANS++, and kNN algorithms using Sentenced Discrepancy Measure (AWPD).
result New algorithms show better results on datasets with missing attributes.
Study on trapped submanifolds in spacetimes, proving rigidity and non-existence results.
problem Rigidity and non-existence of trapped submanifolds in spacetimes.
method Analysis of parabolic spacelike submanifolds with causal mean curvature in orthogonally splitted and globally hyperbolic spacetimes.
result Non-existence of local minima or maxima of certain functions on submanifolds, leading to rigidity results.
Paper proves non-existence of certain balanced metrics on six-manifolds.
problem Existence of balanced metrics on six-manifolds with specific properties.
method Analysis of cohomogeneity one actions and properties of balanced structures.
result Non-existence of balanced non-Kähler SU(3)-structures on six-manifolds.
Study non-existence of complex ball quotients in Torelli locus.
problem Non-existence of totally geodesic complex ball quotients in Torelli locus.
method Analytic techniques.
result Analytic techniques used to study non-existence.
Symphonic maps on non-compact Riemannian manifolds are non-existent.
problem Existence of symphonic maps on compact or non-compact Riemannian manifolds
method Study of conformal vector fields and Ricci solitons
result No symphonic maps exist
Proves non-existence of certain flat manifolds.
problem Non-existence of asymptotically flat 4-manifolds.
method Analyzes conjecture of Petrunin and Tuschmann.
result Proves conjecture on non-existence of asymptotically flat 4-manifolds.
No smooth AdS3 solutions with more than 16 supersymmetries exist.
problem Existence of supersymmetric AdS3 backgrounds with more than 16 supersymmetries.
method Non-existence proof using supergravity theories and compact internal spaces.
result No smooth warped AdS 3 _3 3 solutions preserving more than 16 supersymmetries. The paper proves non-existence results for λ-biharmonic submersions from curved manifolds.
problem Proving non-existence of λ-biharmonic submersions from curved manifolds.
method Analyzing λ-biharmonic Riemannian submersions from (n + 1)-dimensional Riemannian manifolds with constant sectional curvature c.
result Critical value λ= 2(n - 1)c plays a decisive role in the non-existence of λ-biharmonic submersions.
In this short note we show how the higher index theory can be used to prove results concerning the non-existence of complete riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to M. Gromov and B. Lawson we show the efficiency of these methods in dealing with …
Geometric non-commutative geometry proves non-existence of certain metrics.
problem Proving non-existence of metrics of positive scalar curvature on foliations.
method Detailed review and extension of existing results, including new obstructions.
result Extension of non-existence results to non-compact manifolds of bounded geometry.
Suppose M M M is a compact n-dimensional manifold, n ≥ 2 n\ge 2 n ≥ 2 , with a metric g i j ( x , t ) g_{ij}(x,t) g ij ( x , t ) that evolves by the Ricci flow ∂ t g i j = − 2 R i j \partial_tg_{ij}=-2R_{ij} ∂ t g ij = − 2 R ij in M × ( 0 , T ) M\times (0,T) M × ( 0 , T ) . We will give a simple proof of a recent result of Perelman on the non-existence of shrinking breather without using the logarithmic Sobolev inequality.
The study proves non-existence of concave functions on specific metric spaces.
problem Proving the non-existence of concave functions on certain metric spaces.
method Analogue theorems for Alexandrov spaces and C α C^α C α -Hölder Riemannian manifolds. result Proves non-existence of concave functions on complete manifolds with finite volume and specific metric spaces.
We study the steady state solutions of a generalized logistic type equation on a complete Riemannian manifold. We provide sufficient conditions for existence, respectively non-existence of positive solutions, which depend on the relative size of the coefficients and their mutual interaction with the geometry of the man…
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.
Study non-existence of biconservative hypersurfaces in Minkowski spaces.
problem Proving non-existence of biconservative hypersurfaces in Minkowski spaces.
method Conducted rigorous analysis of Codazzi and Gauss equations.
result Established non-existence of biconservative hypersurfaces in Minkowski spaces.
In this paper we provide several uniqueness and non-existence results for complete parabolic constant mean curvature spacelike hypersurfaces in Lorentzian warped products under appropriate geometric assumptions. As a consequence of this parametric study, we obtain very general uniqueness and non-existence results for a…
Study generalizes map properties between Hermitian manifolds preserving specific forms.
problem Understanding maps between Hermitian manifolds that preserve certain forms.
method Generalizing results from Chan-Yuan [2025] to new maps.
result Obtained further rigidity and non-existence theorems.
The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This suggests that the question of existence or non-existence of solutions to the original e…
Study on minimal surfaces in a specific homogeneous space with non-existence and construction results.
problem Minimal surfaces in S L ~ 2 ( R ) {\widetilde{\mathrm{SL}}_2(\mathbb{R})} SL 2 ( R ) with asymptotic boundary conditions. method Non-existence proofs and construction of specific minimal surfaces.
result Existence and non-existence results for minimal surfaces in S L ~ 2 ( R ) {\widetilde{\mathrm{SL}}_2(\mathbb{R})} SL 2 ( R ) . The paper examines conditions for Einstein multiply warped products and estimates their parameters.
problem Existence and non-existence of non-trivial Einstein multiply warped products.
method Analyzes conditions for the existence or non-existence of Einstein multiply warped products, especially generalized Kasner type.
result Estimates the Einstein parameter that conditions the existence of such metrics.
The paper studies conditions for the non-existence of Cannon-Thurston maps in hyperbolic groups.
problem Conditions for the non-existence of Cannon-Thurston maps in hyperbolic groups.
method Sufficient criteria to guarantee geodesic rays land uniquely and do not extend continuously to the boundary.
result Sufficient conditions for the non-existence of Cannon-Thurston maps in hyperbolic groups.
No orthogonal complex structures found on 6-sphere near round metric.
problem Existence of orthogonal complex structures on 6-sphere near round metric.
method Generalized proofs by Bor, Hernandez-Lamoneda, Sekigawa, and Vanhecke.
result Non-existence of orthogonal complex structures for metrics close to the round one.
No Einstein metrics found on certain double disk bundles.
problem Existence of Einstein metrics on specific manifolds.
method Phase space barrier argument to show non-existence.
result Proves non-existence of cohomogeneity one Einstein metrics.
Study proves Higgs fields non-existent on Calabi-Yau manifolds.
problem Proving non-existence of Higgs fields on Calabi-Yau manifolds.
method Used Yang-Mills-Higgs flow to prove Higgs field triviality.
result Higgs field is trivial for semistable Higgs bundles with vanishing Chern classes.
Study on Kähler metrics on ruled surfaces, proving existence and non-existence.
problem Existence and non-existence of Kähler metrics on minimal ruled surfaces.
method Analysis of twisted and coupled constant scalar curvature Kähler metrics.
result Bound for Chen-Cheng invariant on ruled surfaces.
We exhibit a 3-manifold which admits no tight contact structure.
Study shows non-existence of almost complex structures on certain sphere bundles over complex projective spaces.
problem Existence of almost complex structures on sphere bundles over complex projective spaces.
method Chern class computations and divisibility properties of characteristic classes.
result Establishes a necessary condition for the non-existence of almost complex structures on certain bundles.
We discuss the existence and non-existence of cobordisms between symplectic surface bundles over the circle.
Study finds existence and non-existence of large stable CMC spheres in asymptotically flat 3-manifolds.
problem Existence and non-existence of large stable CMC spheres in asymptotically flat 3-manifolds.
method Extends Lyapunov-Schmidt analysis to 'far-off-center' regime and general Schwarzschild asymptotics.
result Sharp existence and non-existence results for large stable CMC spheres.
Classifies Teichmüller curves in specific hyperelliptic components of meromorphic differentials.
problem Classifying Teichmüller curves in hyperelliptic components of meromorphic strata.
method Non-existence criterion based on intersections with moduli space boundary.
result Contradiction to algebraicity of candidate Teichmüller curves outside Hurwitz covers.
Study of translators in solvable group, finding new examples and non-existence.
problem Classifying translators in solvable groups invariant under isometries.
method Classification of translators in S o l 3 Sol_3 S o l 3 using invariant under one-parameter group of isometries. result New graphical translators in S o l 3 Sol_3 S o l 3 on half-planes, contradicting Euclidean translator rigidity. Abstract proof of non-existence of certain types of almost contact metric structures.
problem Proving the non-existence of specific types of almost contact metric structures on manifolds.
method Using interrelations among components of intrinsic torsion to describe exterior derivatives of relevant forms.
result Proof of non-existence of 132 Chinea and González-Dávila types of almost contact metric structures.
Study maximal hypersurfaces in open spacetimes using a maximum principle.
problem Characterize maximal hypersurfaces in open spacetimes.
method Use a generalized maximum principle to analyze hypersurfaces in spatially open Generalized Robertson-Walker spacetimes.
result Provide new uniqueness and non-existence results for complete maximal hypersurfaces in open Robertson-Walker spacetimes.
In this note, we study Liouville type theorem for conformal Gaussian curvature equation (also called the mean field equation) − Δ u = K ( x ) e u , i n R 2 -Δu=K(x)e^u, in R^2 − Δ u = K ( x ) e u , in R 2 where K ( x ) K(x) K ( x ) is a smooth function on R 2 R^2 R 2 . When K ( x ) = K ( x 1 ) K(x)=K(x_1) K ( x ) = K ( x 1 ) is a sign-changing smooth function in the real line R R R , we have a non-existence result for the finite to…
New non-existence results for harmonic maps into perturbed cones.
problem Proper harmonic maps into perturbed cones in \(\mathbb{R}^n\), horospheres in \(\mathbb{H}^n\).
method Extension of foliated maximum principle to non-compact settings.
result New non-existence results for proper harmonic maps.