arXiv research

The study finds minimal hypersurfaces in wedge-shaped manifolds with boundary.

Curvature estimate for stable free boundary minimal hypersurfaces in wedge-shaped manifolds.

Flat minimal hypersurfaces found in wedge-shaped domains.

The paper classifies energy-minimizing sets in specific domains.

Smooth manifolds from locally homogeneous spaces.

Holomorphic structures on Oeljeklaus-Toma manifolds are shown to be locally homogeneous.

Geodesic completeness proven for all compact locally symmetric Lorentz manifolds.

Positive simplicial volume implies locally symmetric space structure.

New local method solves Yamabe problems on compact and non-compact manifolds.

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field) is characterized by their automorphisms. Thus, locally homogeneous multisymplec…

Estimates manifold dimension using local graph structure.

Paper proves stability of positive mass theorem for specific types of manifolds.

A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally conformal Kaehler manifolds as well as Hermitian surfaces with vanishing associated conf…

We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…

It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given i…

Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we explore the extent to which compact locally homogeneous three-manifolds are characte…

Generalizing the notion of local $φ$-symmetry of Takahashi, in the present paper, we introduce the notion of local $φ$-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $φ$-semisymmetry of a Sasakian manifold …

Global and local blowups of manifolds are proven equivalent.

Study local diffeomorphisms of conformal circles in pseudo-Riemannian manifolds.

We show that every Sasakian manifold in dimension $2k+1$ is locally generated by a free real function of $2k$ variables. This function is a Sasakian analogue of the Kähler potential for Kähler geometry. It is also shown that every locally Sasakian-Einstein manifold in $2k+1$ dimensions is generated by a locally Kähler-…

Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…

We will consider locally conformally balanced manifolds. We prove that a locally conformally balanced condition is not stable under a small deformation. We prove that locally conformally balanced condition is stable under any proper modification. We prove that symmetric products of the Kodaira surface can be resolve to…

A local classification of locally conformal flat Riemannian Einstein-like four-manifolds as well as a local classification of all locally conformal flat Riemannian four-manifolds for which all Jacobi operators have parallel eigenspaces along every geodesic is given. Non-trivial explicit examples are presented. The prob…

In this work we prove that every locally symmetric smooth submanifold gives rise to a naturally defined smooth submanifold of the space of symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs to the locally symmetric manifold. We also present an explicit f…

A manifold is locally \emph{$k$-fold symmetric}, if for any point and any $k$-dimensional vector subspace tangent to this point there exists a local isometry such that this point is a fixed point and the differential of the isometry restricted to that $k$-dimensional vector subspace is minus the identity. We show that …

Topological manifolds can be embedded flatly in high-dimensional Euclidean space and are locally retracts.

New results on localization of exotic diffeomorphisms in 4-manifolds.

Study bifurcations and local rigidity on flag manifolds for Yamabe solutions.

We give the parallelism between locally conformal symplectic manifolds and contact manifolds. We also give the generalization of exact contact manifolds.

Local Sasaki-Ricci solitons are $η$-Einstein in certain fiber products of homogeneous Sasakian manifolds.

Investigate local Lie group structure of bisections over compact manifolds

Localized deformation of scalar curvature and mean curvature on manifolds.

Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.

The paper proves a generalized Lefschetz duality for a specific type of manifold.

New compact examples of pseudo-Kähler manifolds with essential conformal transformations found.

Constructs a map with prescribed local Lipschitz constants on a subset of a manifold.

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…

New compact ECS manifolds with rank 2 discovered, differing from previous rank 1 examples.

Localized min-max method proves minimal hypersurface existence.

We prove that a compact toric locally conformally Kähler manifold which is not Kähler admits a toric Vaisman structure, a fact which was conjectured in \cite{mmp}. This is the final step leading to the classification of compact toric locally conformally Kähler manifolds started in \cite{p} and \cite{mmp}. We also show,…

In this paper, we study the blow-up of a locally conformal symplectic manifold.We show that there exists a locally conformal symplectic structure on the blow-up of a locally conformal symplectic manifold along a compact induced symplectic submanifold.

We use the reflection group trick to glue manifolds with corners that are Borel-Serre compactifications of locally symmetric spaces of noncompact type and obtain aspherical manifolds. We call these \emph{piecewise locally symmetric} manifolds. This class of spaces provide new examples of aspherical manifolds whose fund…

This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.

The article proves charged quasi-local Penrose inequalities for compact manifolds with boundary.

Study local commutation relation on almost complex manifolds.

We classify those curvature-homogeneous Einstein four-manifolds, of all metric signatures, which have a complex-diagonalizable curvature operator. They all turn out to be locally homogeneous. More precisely, any such manifold must be either locally symmetric or locally isometric to a suitable Lie group with a left-inva…

Global and local estimates for a curvature equation on manifolds with boundary.

Local Kan conditions enable differentiation of simplicial manifolds.