arXiv research

Study shows conditions for nonexistence of solutions in Riemannian geometry.

Investigates noncompact warped product Ricci solitons, proving nonexistence results.

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.

The paper proves nonexistence results for certain parabolic inequalities on Riemannian manifolds.

Nonexistence results for semilinear parabolic and hyperbolic inequalities on metric graphs

Paper proves no nontrivial solutions to certain elliptic equations on graphs.

Paper explores existence and nonexistence of submanifolds in contact geometry.

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 $δ=2$

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.

Proves triviality and nonexistence of gradient Ricci solitons as warped metrics.

In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension \(m=\dim M\geq 3\) with infinite volume that admit an Euclidean type Sobolev inequality into general Riemannian manifolds by assuming finiteness of $\|τ(φ)\|_{L^p(M)}, p>1$ and smallness of…

The study constructs gradient Einstein-type warped metrics and proves nonexistence and rigidity results.

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.

In this paper we are concerned with a class of elliptic differential inequalities with a potential in bounded domains both of $\mathbf{R}^m$ and of Riemannian manifolds. In particular, we investigate the effect of the behavior of the potential at the boundary of the domain on nonexistence of nonnegative solutions.

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.

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 …

The study proves symplectic quandles cannot have good involutions.

The abstract shows how embeddings inscribe trapezoids or map three points to a line, proving nonexistence of certain maps.

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…

Study proves existence and nonexistence for annular surfaces with specific curvature and boundary.

Study on real hypersurfaces in products of complex space forms, proving rigidity and nonexistence results.

The paper proves nonexistence results for translating solitons in r-mean curvature flow.

The paper proves Liouville theorems and nonexistence results for semilinear equations on pseudo-Hermitian manifolds.

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 prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to the complex plane in any complete orientable four-dimensional Riemannian manifold with uniformly positive isotropic curvature. We also generalize the same nonexistence result to higher dimensions provided that the ambient …

The paper proves unique properties of Riemannian twistor spaces under specific curvature conditions.

We investigate, for the Laplacian operator, the existence and nonexistence of eigenfunctions of eigenvalue between zero and the first eigenvalue of the hyperbolic space H^n, for unbounded domains of H^n. If a domain is contained in a horoball, we prove that there is no positive bounded eigenfunction that vanishes on th…

Nonexistence of quasi-harmonic spheres is necessary for long time existence and convergence of harmonic map heat flows. Let $(N,h)$ be a complete noncompact Riemannian manifolds. Assume the universal covering of $(N,h)$ admits a nonnegative strictly convex function with polynomial growth. Then there is no quasi-harmoni…

New inequality controls domain volume for manifolds with large spectrum.

The aim of this work is to prove the nonexistence of complex structures over nilpotent Lie algebras of maximal class (also called filiform).

Let $u: (M, g)\to (N, h)$ be a map between Riemannian manifolds $(M, g)$ and $(N, h)$. The $p$-bienergy of $u$ is defined by $E_p(u)=\int_M|τ(u)|^pdν_g$, where $τ(u)$ is the tension field of $u$ and $p>1$. Critical points of $E_p(\cdot)$ are called $p$-biharmonic maps. In this paper we will prove nonexistence result of…

In this paper we prove the following theorem. Main Theorem. Let n >= 3 and m >= 3n/2 +7. Then there exists no C^m Levi-flat real hypersurface M in P_n. The condition that M is Levi-flat means that when M is locally defined by the vanishing of a C^m real-valued function f, at every point of M the restriction of d d-bar …

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.

The paper studies nonlocal isoperimetric problems in hyperbolic space and finds unique minimizers for small volumes.

Nonexistence of radial optimal functions on certain Cartan-Hadamard manifolds.

Study proves steady state space hypersurfaces are hyperplanes under certain curvature constraints.

The paper explores stable surfaces in Einstein-Maxwell theory, proving mass bounds and nonexistence results.

In curved spaces, isoperimetric sets don't exist for small volumes.

The paper explores nonexistence and existence of symplectic and Stein fillable contact structures on 3-manifolds.

We generalize the famous result of Gromov and Lawson on the nonexistence of metric of positive scalar curvature on enlargeable manifolds to the case of foliations, without using index theorems on noncompact manifolds.

We give a necessary and sufficient condition for the addition of a collection of disjoint bypasses to a convex surface to be universally tight -- namely the nonexistence of a polygonal region which we call a virtual pinwheel.

We introduce and study generalized $1$-harmonic equations (1.1). Using some ideas and techniques in studying $1$-harmonic functions from [W1] (2007), and in studying nonhomogeneous $1$-harmonic functions on a cocompact set from [W2, (9.1)] (2008), we find an analytic quantity $w$ in the generalized $1$-harmonic equatio…

New invariant prevents minimal submanifolds in curved spaces.

Let $Ω$ be a pseudoconvex domain with $C^2$-smooth boundary in $\mathbb CP^n$. We prove that the $\bar\partial-Neumann operator$N$exists for$(p,q)$-forms on$Ω$. Furthermore, there exists a$t_0>0$such that the operators$N$,$\bar\partial^*N$,$\bar\partial N$ and the Bergman projection are regular in the Sobolev …

We provide examples of families of (log) smooth canonically polarized varieties, including smooth weighted pointed curves and smooth hypersurfaces in $P^3$ with large degree such that the Chow semistable limits under distinct pluricanonical embeddings do not stabilize.

We prove that there does not exist any semi-parallel real hypersurface in complex two-plane Grassmannians. With this result, the nonexistence of recurrent real hypersurfaces in complex two-plane Grassmannians can also be 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.