arXiv research

Classifies Teichmüller curves in specific hyperelliptic components of meromorphic differentials.

The paper studies conditions for the non-existence of Cannon-Thurston maps in hyperbolic groups.

The study proves conditions for nontrivial solutions on Riemannian manifolds.

Study on stable minimal hypersurfaces under Ricci curvature constraints.

We show that on an HKT manifold the holonomy of the Obata connection is contained in SL(n,H) if and only if the Lee form is an exact one form. As an application, we show compact HKT manifolds with holomorphically trivial canonical bundle which are not balanced. A simple criterion for non-existence of HKT metric on hype…

We study the Dirichlet problem for minimal surface systems in arbitrary dimension and codimension via mean curvature flow, and obtain the existence of minimal graphs over arbitrary mean convex bounded $C^2$ domains for a large class of prescribed boundary data. This result can be seen as a natural generalization of the…

Paper finds a non-existence theorem for certain translators in high dimensions.

Study finds both existence and non-existence of maps in Morse boundaries.

Following \cite{citeSavelyevVirtualMorsetheoryon$Omega$Ham$(Momega)$.}, we develop here a connection between Morse theory for the (positive) Hofer length functional $L: Ω\text {Ham}(M, ω) \to \mathbb{R}$, with Gromov-Witten/Floer theory, for monotone symplectic manifolds $(M, ω)$. This gives some immediate restrictio…

Paper generalizes Bakry-Émery calculus for curvature and applies to Markov chains.

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.

This paper establishes geometric obstructions to the existence of complete, properly embedded, mean curvature flow self-translating solitons $Σ^n\subseteq \mathbb{R}^{n+1}$, generalizing previously known non-existence conditions such as cylindrical boundedness.

This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even function on a Riemannian manifold with a pole and proved the non-existence of non-trivial and non-negative differentiable odd convex fun…

Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.

Paper proves non-existence of certain hypersurfaces in complex quadric.

New technique clusters and classifies datasets with missing attributes.

In this paper we study the non-existence of solutions to the Dirichlet problem for minimal graphs of codimension $\geq 2$, including certain situations over domain $Ω$ even with non-$C^1$ boundary $\partial Ω$.

Study on trapped submanifolds in spacetimes, proving rigidity and non-existence results.

Paper proves non-existence of certain balanced metrics on six-manifolds.

Study non-existence of complex ball quotients in Torelli locus.

Symphonic maps on non-compact Riemannian manifolds are non-existent.

Proves non-existence of certain flat manifolds.

In this paper, we derive a mean curvature estimate for eternal solutions (including translating solutions) of almost-calibrated Lagrangian mean curvature flow in complex Euclidean space. As a consequence, we show a non-existence result for eternal solutions of almost-calibrated Lagrangian mean curvature flow.

The paper proves non-existence results for λ-biharmonic submersions from curved manifolds.

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 …

I review several proofs for non-existence of orthogonal complex structures on the six-sphere, most notably by G. Bor and L. Hernandez-Lamoneda, but also by K. Sekigawa and L. Vanhecke that we generalize for metrics close to the round one. Invited talk at MAM-1 workshop, 27-30 March 2017, Marburg.

Suppose $M$ is a compact n-dimensional manifold, $n\ge 2$, with a metric $g_{ij}(x,t)$ that evolves by the Ricci flow $\partial_tg_{ij}=-2R_{ij}$ in $M\times (0,T)$. 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.

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.

Study 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.

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.

The possible existence of a complex structure on the 6-sphere has been a famous unsolved problem for over 60 years. In that time many "solutions" have been put forward, in both directions. Mistakes have always been found. In this paper I present a short proof of the non-existence, based on ideas developed, but not full…

The paper examines conditions for Einstein multiply warped products and estimates their parameters.

No Einstein metrics found on certain double disk bundles.

We exhibit a 3-manifold which admits no tight contact structure.

Study on Kähler metrics on ruled surfaces, proving existence and non-existence.

We discuss the existence and non-existence of cobordisms between symplectic surface bundles over the circle.

Study shows non-existence of almost complex structures on certain sphere bundles over complex projective spaces.

Study maximal hypersurfaces in open spacetimes using a maximum principle.

In this note, we study Liouville type theorem for conformal Gaussian curvature equation (also called the mean field equation) $-Δu=K(x)e^u, in R^2$ where $K(x)$ is a smooth function on $R^2$. When $K(x)=K(x_1)$ is a sign-changing smooth function in the real line $R$, we have a non-existence result for the finite to…

New non-existence results for harmonic maps into perturbed cones.

The study finds no extremal metrics for eigenvalues on compact manifolds but constructs examples for annuli.

New general results of non-existence and rigidity of spacelike submanifolds immersed in a spacetime, whose mean curvature is a time-oriented causal vector field, are given. These results hold for a wide class of spacetimes which includes globally hyperbolic, stationary, conformally stationary and pp-wave spacetimes, am…