arXiv research

Study on the convergence rate of prescribed scalar curvature flow.

In this work, we study the Yamabe flow corresponding to the prescribed scalar curvature problem on compact Riemannian manifolds with negative scalar curvature. The long time existence and convergence of the flow are proved under appropriate conditions on the prescribed scalar curvature function.

We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the case of asymptotically hyperbolic manifolds and restrict ourselves to non positive prescribed scalar curvature. Following earlier results, we o…

Paper investigates prescribing Chern scalar curvatures on specific manifolds.

Proves Chen-Lin conjecture for sphere scalar curvature problem.

Paper explores prescribing Chern scalar curvatures on noncompact Hermitian manifolds.

In this paper, we consider the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function $f$, which is allowed to change sign, satisfies some kind of Morse index or symmetry condition. By studying the well-known scalar curvature flow, we are able to prove that the flow converges …

Study proves curvature flow existence on CR manifolds.

Solves Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space

Study prescribed scalar curvature on orbifolds with isolated singularities.

Study of prescribing scalar curvature and mean curvature on compact manifolds with boundary.

Researchers solve the negative Yamabe case for scalar curvature prescription.

We give a proof of the Kazdan-Warner conjecture concerning the prescribed scalar curvature problem in the null case.

The paper explores constant holomorphic d-scalar curvature on specific manifolds.

The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.

We solve the modified Kazdan-Warner problem of finding metrics with prescribed scalar curvature and unit total volume.

Paper solves Gauduchon scalar curvature problem on almost Hermitian manifolds.

Conditions for scalar curvature on compact manifolds under conformal deformation.

Study on prescribing curvature on specific manifolds with negative Gauduchon degree.

We prove a priori interior curvature estimates for hypersurfaces of prescribing scalar curvature equations in dimension three. The method is motivated by the integral method of Warren and Yuan. The new observation here is that the "Lagrangian" submanifold constructed similarly as Harvey and Lawson has bounded mean curv…

In this paper, we consider the indefinite scalar curvature problem on $R^n$. We propose new conditions on the prescribing scalar curvature function such that the scalar curvature problem on $R^n$ (similarly, on $S^n$) has at least one solution. The key observation in our proof is that we use the bifurcation method to g…

On Riemannian manifolds of dimension 4, for prescribed scalar curvature equation, under lipschitzian condition on the prescribed curvature, we have an uniform estimate for the solutions of the equation if we control their minimas.

We prove existence and uniqueness of entire spacelike hypersurfaces in the Minkowski space with prescribed negative scalar curvature, and with given values at infinity which stay at a bounded distance of a lightcone.

We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results.

In this paper,we obtain two results on closed Reimainnian manifold $M\times [0,T]$.When $T$ is small enough,to any prescribed scalar curvature, the existence and uniqueness of metrics are obtained on the volume element preserving deformation.When $T$ is large and the given scalar curvature is small enough,the same resu…

Study noncompact manifolds' Chern scalar curvatures, proving existence and multiplicity.

Unified flow approach to curvature problem on specific manifolds.

Study on scalar curvature minimizability loss and saddle point solutions.

Study finds infinitely many non-radial solutions for negative scalar curvature in higher dimensions.

Let $(M^{n},g_{0})$ be a $n=3,4,5$ dimensional, closed Riemannian manifold of positive Yamabe invariant. For a smooth function $K>0$ on $M$ we consider a scalar curvature flow, that tends to prescribe $K$ as the scalar curvature of a metric $g$ conformal to $g_{0}$. We show global existence and in case $M$ is not confo…

Researchers examine global properties of a scalar curvature functional to solve the prescribed Ricci curvature problem.

Study curvatures on compact pseudo-Hermitian manifolds using special methods.

Study shows incompatibility of certain scalar curvatures on manifolds.

Directly applies Kazdan--Warner results to prescribe scalar curvature on bundles.

The existence of a smooth complete strictly locally convex hypersurface with prescribed scalar curvature and asymptotic boundary at infinity in $\mathbb{H}^{3}$ is proved under the assumption that there exists a strictly locally convex subsolution.

The study proves manifold properties related to positive scalar curvature.

Solves a problem in Riemannian geometry for scalar-flat metrics with boundary conditions.

We illustrate an example of a generic, positive function K on a Riemannian manifold to be conformally prescribed as the scalar curvature, for which the corresponding Yamabe type L2-gradient flow exhibits non compact flow lines, while a slight modification of it is compact.

Study finds conditions for metrics on curved spaces.

This paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results on the standard half sphere.

The paper solves a problem related to curvature in complex geometry.

Study local properties of Chern-scalar curvature through linearization stability.

We prove the existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds provided there are barriers.

The study of radial prescribing scalar curvature of X.Xu and P.C.Yang [2] in 1993 showed a nonexistence result on $S^2$. Later in 1995, W.Chen and C.Li [2] generalized the nonexistence result to higher dimensions. G.Bianchi and E.Egnell [1] suggested that there may exist some non-negative smooth radial function which c…

We give existence results for solutions of the prescribed scalar curvature equation on $S^3$, when the curvature function is a positive Morse function and satisfies an index-count condition.

The paper solves conditions for prescribing scalar and Gauss curvatures on manifolds with zero first eigenvalue.

The mixed scalar curvature is one of the simplest curvature invariants of a foliated Riemannian manifold. We explore the problem of prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the structure in tangent and normal to the leaves directions. Under certain geometrical …

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacel…