arXiv research

Study constant mean curvature surfaces with integrable boundary conditions.

The classification of Finsler spaces of constant curvature is an interesting and important topic of research in differential geometry. In this paper we obtain necessary and sufficient conditions for generalized Kropina space to be of constant flag curvature.

Conditions ensure constant curvature in negatively curved manifolds.

The study pinches conditions for constant mean curvature surfaces in convex 3-manifolds.

The pluriclosed flow preserves Vaisman condition on compact complex surfaces.

The paper finds conditions for certain hypersurfaces to be totally umbilical.

The abstract finds conditions for creating curves of constant curvature.

The paper explores rigidity of hypersurfaces with constant curvature in Euclidean spaces.

Paper shows k-Yamabe solitons have constant curvature under certain conditions.

New findings show cosmological constant as initial condition for non-isotropic spacetimes.

Paper proves existence of unique constant scalar curvature Kähler metric under certain conditions.

In this paper, we show that the peeling property still holds for Bondi-Sachs metrics with nonzero cosmological constant under the boundary condition given by Sommerfeld's radiation condition together with three nontrivial $Λ$-independent functions $B$, $a$, $b$. This should indicate the new boundary condition is natura…

Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.

Proves compact Cauchy horizons have constant surface gravity under null energy condition.

The study explores metrics with constant curvature on compact manifolds.

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the conditi…

Compact spacelike hypersurface with constant curvature and boundary angles must be part of a hyperboloid.

Let X --> B be a holomorphic submersion between compact Kahler manifolds of any dimension, whose fibres and base have no non-zero holomorphic vector fields and whose fibres all admit constant scalar curvature Kahler metrics. This article gives a sufficient topological condition for the existence of a constant scalar cu…

The paper establishes curvature inequalities and rigidity results for surfaces in Riemannian and Lorentzian geometry.

The paper establishes curvature inequalities and rigidity results for CMC and STCMC surfaces in Riemannian and Lorentzian geometry.

Study local foliations of surfaces with constant mean curvature and constant expansion in space-time.

Modified condition proves no positive scalar curvature for enlargeable manifolds.

In this paper conditions for a Kropina structure to be of constant flag curvature are obtained.

The paper explores rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.

In this paper, we generalize Magnanini-Sakaguchi's result [MS3] from Euclidean space to spaces of constant curvature. More precisely, we show that if a conductor satisfying the exterior geodesic sphere condition in the space of constant curvature has initial temperature 0 and its boundary is kept at temperature 1 (at a…

Identifies null hypersurfaces with constant surface gravity.

In this paper, we study eigenvalues and eigenfunctions of $p$-Laplacians with Dirichlet boundary condition on graphs. We characterize the first eigenfunction (and the maximum eigenfunction for a bipartite graph) via the sign condition. By the uniqueness of the first eigenfunction of $p$-Laplacian, as $p\to 1,$ we ident…

In this note we characterize compact hypersurfaces of dimension $n\geq 2$ with constant mean curvature $H$ immersed in space forms of constant curvature and satisfying an optimal integral pinching condition: they are either totally umbilical or, when $n\geq 3$ and $H\neq 0$, they are locally contained in a rotational h…

Study proves radial symmetry of solutions to certain nonlinear equations in space forms.

New sprays of constant curvature introduced; conditions for metrizability given.

In this paper we characterize sprays that are metrizable by Finsler functions of constant flag curvature. By solving a particular case of the Finsler metrizability problem we provide the necessary and sufficient conditions that can be used to decide whether or not a given homogeneous system of second order ordinary dif…

There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of conformally flat 3-metrics with the Guichard condition: for a conformally flat …

The paper proves the existence of constant mean curvature disks with capillary boundary conditions.

The study examines properties of $f$-contact manifolds with constant curvature.

The study classifies and constructs examples of surfaces with specific curvature and boundary conditions.

In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice.

Paper finds conditions for non-Einstein relative Yamabe metrics.

Study on metrics of surfaces with curvature and boundary conditions.

The Hopf fibration is rigid among minimal maps between spheres.

Stability of black holes proven in full subextremal range with positive cosmological constant.

We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which are all satisfied if the manifold is curvature homogeneous. This leads to a comp…

New PG methods tackle nonconvex optimization with auto-conditioned stepsizes.

We show that under certain curvature conditions of the ambient space an entire Killing graph of constant mean curvature lying inside a slab must be a totally geodesic slice.

It is conjectured that the existence of constant scalar curvature Kähler metrics will be equivalent to K-stability, or K-polystability depending on terminology (Yau-Tian-Donaldson conjecture). There is another GIT stability condition, called the asymptotic Chow polystability. This condition implies the existence of bal…

The paper modifies a warped product space to find conditions for constant height functions.

The paper studies constant $k$th-mixed curvature on Hermitian manifolds and finds self-duality and Kähler conditions.

We study the conditions under which a Kählerian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^*M$ of a Riemannian manifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that a certain parameter involved in the condition for $(T^*M,G,J)$ to be a Kählerian manifold, is expres…

The study finds conditions for Kaehler-Einstein and cscK metrics on certain manifold coverings.