Nonexistence results for semilinear parabolic and hyperbolic inequalities on metric graphs
problem Nonexistence of solutions to semilinear parabolic and hyperbolic inequalities on metric graphs
method Construction of a new pseudo-metric and space-time test functions
result All solutions must be identically zero
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.
Paper proves no nontrivial solutions to certain elliptic equations on graphs.
problem Proving nonexistence of solutions to semilinear elliptic equations on metric graphs.
method Constructed a modified distance function and introduced test functions to show nonexistence under volume growth conditions.
result No nontrivial solutions exist for the equations under suitable conditions.
Proves triviality and nonexistence of gradient Ricci solitons as warped metrics.
problem Proving triviality and nonexistence of gradient Ricci solitons as warped metrics.
method Proved through the construction of gradient Ricci solitons as warped products and studying Ricci-Hessian type manifolds.
result Gradient Ricci solitons are trivial and non-existent as warped metrics.
The study constructs gradient Einstein-type warped metrics and proves nonexistence and rigidity results.
problem Proving nonexistence and rigidity for gradient Einstein-type warped metrics.
method Establishing necessary and sufficient conditions for constructing these metrics, leading to a Lichnerowicz equation.
result Nonexistence and rigidity results for a class of gradient Einstein-type warped metrics.
Authors compute Morse-Novikov cohomology for Inoue surfaces and prove nonexistence of certain metrics.
problem Computing and classifying locally conformally Kähler metrics on complex surfaces.
method Review and computation of Morse-Novikov cohomology for known surfaces.
result Nonexistence of LCK metrics with potential on Inoue surfaces and Oeljeklaus-Toma manifolds.
We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter δ=2
By using the gluing formulae of the Seiberg-Witten invariant, we show the nonexistence of Einstein metric on manifolds obtained from a 4-manifold with nontrivial Seiberg-Witten invariant by performing sufficiently many connected sums or appropriate surgeries along circles or homologically trivial 2-spheres with closed …
In this article, we give nonexistence and nonuniqueness results for the vacuum Einstein conformal constraint equations in the far-from-CMC case and also show that in some cases the equations of the conformal method for positive Yamabe metrics and with TT-tensor σ = 0 have a non-trivial solution, and thus answer a que…
A new class of Higgs bundles is introduced in a natural setting. Existence and nonexistence results for Higgs-Hermitian-Yang-Mills metrics are proved.
We provide new conditions that ensure that two metric measure spaces are not quasiconformally equivalent. As an application we deduce that there exists no quasiconformal map between the sub-Riemannian Heisenberg and roto-translation groups.
We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces and prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces
In this paper, we show that the nonexistence of rotationally symmetric harmonic diffeomorphism between the unit disk without the origin and a punctured disc with hyperbolic metric on the target.
Study shows no hidden symmetries in specific spacetime metrics.
problem Demonstrating the absence of Killing tensors in Koutras-McIntosh spacetimes.
method Geometric theory of overdetermined PDEs and Cartan prolongation-projection method.
result No Killing tensors of low degrees in Wils metrics and generic pp-waves.
Study shows conditions for nonexistence of solutions in Riemannian geometry.
problem Nonexistence of global solutions for quasilinear parabolic problems.
method Test function argument to identify parameter ranges for nonexistence.
result Explicit parameter ranges where nonexistence holds.
Investigates noncompact warped product Ricci solitons, proving nonexistence results.
problem Proving nonexistence results for noncompact warped product Ricci solitons.
method Proves nonexistence results using pde estimates and properties of the first eigenvalue of a weighted Laplacian.
result Nonexistence theorem for shrinking Ricci solitons.
Conditions for flat 3-manifolds with diagonal metrics are identified.
problem Characterizing flat 3-manifolds with diagonal metrics.
method Provided necessary and sufficient conditions for flatness.
result Characterized flat manifolds of warped product-type.
Paper investigates nonexistence of solutions for elliptic inequalities with potential in bounded domains.
problem Effect of potential behavior at domain boundaries on nonexistence of nonnegative solutions.
method Investigates elliptic differential inequalities with a potential in bounded domains.
result Nonexistence of nonnegative solutions due to potential behavior at domain boundaries.
We provide an example of a zero-dimensional compact metric space X and its closed subspace A such that there is no continuous linear extension operator for the Lipschitz pseudometrics on A to the Lipschitz pseudometrics on X. The construction is based on results of A. Brudnyi and Yu. Brudnyi concerning linear e…
In this paper, we will prove a result of nonexistence on harmonic diffeomorphisms between punctured spaces. In particular, we will given an elementary proof to the nonexistence of rotationally symmetric harmonic diffeomorphisms from the punctured Euclidean space onto the punctured hyperbolic space.
We show that the results of Foulon (1997 an 2002) and Kim (2007) (independently, Deng and Hou (2007)) about the nonexistence of locally symmetric Finsler metrics of positive or negative flag curvature are in fact local.
The paper proves nonexistence results for certain parabolic inequalities on Riemannian manifolds.
problem Proving nonexistence results for parabolic inequalities on Riemannian manifolds.
method Using a test function argument and weighted volume growth assumptions.
result Established Liouville-type theorems for (p,q)-Laplacian operator inequalities. The study proves nonexistence of proper biharmonic maps under certain conditions.
problem Proper biharmonic maps from specific types of manifolds.
method Using Sobolev inequalities and finite volume conditions.
result Nonexistence of proper biharmonic maps under given constraints.
We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces, prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces, and prove t…
New rule for positive curvature on foliations.
problem No metric of positive scalar curvature on enlargeable foliations.
method Generalization of Gromov-Lawson's result to foliations.
result Positive scalar curvature on enlargeable foliations is impossible.
We discuss the existence of Killing tensors for certain (physically motivated) stationary and axially symmetric vacuum space-times. We show nonexistence of a nontrivial Killing tensor for a Tomimatsu-Sato metric (up to valence 7), for a C-metric (up to valence 9) and for a Zipoy-Voorhees metric (up to valence 11). The …
Let M be a compact Kähler manifold and N be a subvariety with codimension greater than or equal to 2. We show that there are no complete Kähler--Einstein metrics on M−N. As an application, let E be an exceptional divisor of M. Then M−E cannot admit any complete Kähler--Einstein metric if blow-down of E is…
Paper explores existence and nonexistence of submanifolds in contact geometry.
problem Existence and nonexistence of warped product submanifolds in almost contact manifolds.
method Generalizes results for existence and nonexistence, constructs examples, addresses open problems.
result Offers decisive results for existence and nonexistence of submanifolds.
This is a continuous work about the nonexistence of some complete metrics on the product of two manifolds studied by Tam-Yu [Asian Journal of Mathematics, 14(2010)]. Motivated by the result of Tossati [Comm.Anal.Geom. 15(2007)]. We generalize the corresponding results of Tam-Yu [Asian Journal of Mathematics, 14(2010)] …
Abstract: Shows nonexistence of Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.
problem Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.
method Constructs a metric on a compact manifold to demonstrate the nonexistence of Courant-type bounds.
result Provides a negative answer to the existence of Courant-type nodal domain bounds.
Paper proves no stable Yang-Mills fields on spheres.
problem Existence of stable Yang-Mills fields on spheres.
method Analyzes C2 neighborhoods of Euclidean sphere metrics and warped product manifolds. result No nontrivial weakly stable Yang-Mills connections in specified neighborhoods.
We prove the Lefchetz theorem for CR submanifolds in Hermitian symmetric spaces. As an application we prove the nonexistence of real analytic Levi flat submanifolds in such manifolds.
Gradient estimates for nonlinear parabolic equations on metric spaces.
problem Nonexistence of positive solutions to nonlinear parabolic equations.
method Local elliptic and parabolic gradient estimates.
result Conditions guaranteeing the nonexistence of nontrivial positive solutions.
Study on curvature properties and Shafarevich conjecture for complex hyperbolic manifolds.
problem Existence and nonexistence of Kähler metrics with nonpositive curvature on toroidal compactifications.
method Analysis of toroidal compactifications of finite volume complex hyperbolic manifolds, verification of Shafarevich conjecture.
result Verification of Shafarevich conjecture for compactifications of quotients of complex hyperbolic space by non-uniform arithmetic lattices.
Study on Einstein metrics on complex projective spaces with specific group actions.
problem Finding Einstein metrics invariant under cohomogeneity one Lie group actions.
method Analyzing Einstein equation for diagonal invariant metrics under five Takagi models.
result Nonexistence of smooth globally defined invariant Einstein metrics in four models, necessary condition in the fifth.
The paper links stochastic completeness to uniqueness and nonexistence in fast diffusion equations on manifolds.
problem Uniqueness and nonexistence of bounded solutions in fast diffusion equations.
method Equivalence of stochastic completeness to uniqueness of solutions to nonlinear evolution equations and nonexistence of bounded solutions to elliptic equations.
result Explicit criteria for uniqueness and nonexistence of bounded solutions to fast diffusion equations on manifolds.
This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results for complete solutions of scalar curvature equation.
The paper proves nonexistence of harmonic and bi-harmonic maps under specific conditions.
problem Existence of harmonic and bi-harmonic maps into certain Riemannian manifolds.
method Analysis of manifolds with conformal vector fields or Ricci solitons.
result Nonexistence of harmonic and bi-harmonic maps in specified conditions.
In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a non-equidimensional surjective holomorphic map between compact ball quotients, our…
The study proves that certain manifolds with boundary cannot have metrics with positive intermediate curvatures.
problem Proving the nonexistence of metrics with positive intermediate curvatures on manifolds with boundary.
method Curvature obstruction theorems for manifolds with boundary.
result Topologically nontrivial compact manifolds with boundary cannot have metrics of positive m-intermediate curvature if the boundary is m-convex. In this paper we are concerned with a class of elliptic differential inequalities with a potential both on $\erre^m$ and on Riemannian manifolds. In particular, we investigate the effect of the geometry of the underlying manifold and of the behavior of the potential at infinity on nonexistence of nonnegative solutions.
The abstract shows how embeddings inscribe trapezoids or map three points to a line, proving nonexistence of certain maps.
problem Proving the nonexistence of affinely 3-regular maps in infinitely many dimensions.
method Elementary proof using embeddings and nonsingular bilinear maps.
result Recovery of nonexistence results for affinely 3-regular maps without complex algebraic techniques.
The study proves symplectic quandles cannot have good involutions.
problem Existence of good involutions in symplectic quandles.
method Investigation of necessary and sufficient conditions for good involutions.
result Nonexistence of good involutions in symplectic quandles.
Holomorphic disks on compact Lagrangian surfaces are shown to exist.
problem Existence of holomorphic disks on compact Lagrangian surfaces.
method Analyzes compact Lagrangian surfaces in Kähler manifolds with specific curvature properties.
result Existence of holomorphic disks whose boundary is freely homotopic to a given class in the fundamental group.
This paper proves nonexistence of proper p-biharmonic maps for p≥2.
problem Proving nonexistence of proper p-biharmonic maps for p≥2. method Analyzing p-biharmonic maps using tension fields and integral conditions. result Nonexistence of proper p-biharmonic maps for p≥2. Study on prescribing positive curvature with conical singularities on a sphere.
problem Prescribing positive curvature with conical singularities on a sphere.
method Fine analysis of bubble trees and an area identity in the convergence process.
result Criterion for nonexistence in an open region of the prescribing data.
Study proves existence and nonexistence for annular surfaces with specific curvature and boundary.
problem Existence and nonexistence of annular surfaces with prescribed mean curvature.
method Proves existence and nonexistence results for normal graphs of unduloids or nodoids.
result Existence and nonexistence results for annular type surfaces with prescribed mean curvature.
Study examines homology of contact CR-submanifolds in complex Euclidean space.
problem Investigating the homology of contact CR-submanifolds.
method Analyzes stable integral currents and homology groups of contact CR-submanifolds in Cm. result Nonexistence of stable integral currents and vanishing theorems for homology groups.