arXiv research

Proof of Kazdan-Warner identity using Minkowski spacetime.

The classical Pohozaev identity constrains potential solutions of certain semilinear PDE boundary value problems. The Kazdan-Warner identity is a similar necessary condition important for the Nirenberg problem of conformally prescribing scalar curvature on the sphere. For dimensions $n\geq 3$ both identities are captur…

Study identifies obstructions for solving a 4th-order boundary problem.

In this note, we prove two Kazdan-Warner type identities involving $v^{(2k)}$, the renormalized volume coefficients of a Riemannian manifold $(M^n,g)$, and $G_{2r}$, the so-called Gauss-Bonnet curvature, and a conformal Killing vector field on $(M^n,g)$. In the case when the Riemannian manifold is locally conformally f…

The paper proves compactness of metrics on spheres with isolated singularities.

We prove in this article that the local image of each conformal $Q$-curvature operator of arbitrary order on the sphere admits no scalar constraint. However, we prove that identities of Kazdan--Warner type hold for its graph.

Study Kazdan-Warner equations on graphs using Brouwer degree theory.

Two methods find at least two solutions to Kazdan-Warner's problem on surfaces.

The paper solves the Kazdan-Warner equation on graphs for negative c values.

We prove a Pohozaev type identity for non-linear eigenvalue equations of the Dirac operator on Riemannian spin manifolds with boundary. As an application, we obtain that the mean curvature H of a conformal immersion S^{n}-> R^{n+1} satisfies $\int \partial_X H=0$ where X is a conformal vector field on S^{n} and where t…

Solves generalized Kazdan-Warner equations on foliated manifolds.

In this paper we introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution of this flow, discuss its convergence and possible applications, and its relation to the …

Study on compact Kähler surfaces for sign-changing curvatures.

Study of vortex equations' limits on growing surfaces.

This paper solves the Christoffel problem in hyperbolic space and its equivalent on spheres.

New equations on manifolds linked to torus actions, proving existence and uniqueness.

New Kazdan-Warner problem for equivariant metrics on manifolds.

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

The paper solves the p-th Kazdan-Warner equation on graphs.

Global existence and convergence proved for Kazdan-Warner equation with non-negative prescribed function.

The Kazdan-Warner problem is solved for Riemann surfaces with smooth boundaries.

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

Symplectic vortex equations link Sasakian manifolds to Kahler cones.

The paper tackles prescribing discrete Gaussian curvature on polyhedral surfaces.

The paper proves existence of solutions to Kazdan-Warner equations on finite graphs.

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

The paper solves curvature prescription problems on balls and disks.

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

The paper proves a theorem for discretizing Gaussian curvature on surfaces.

Extends existence results for scalar curvature on conical manifolds.

In this paper, we consider the scalar curvature of Yamabe solitons. In particular we show that, with natural conditions and non positive Ricci curvature, any complete Yamabe soliton has constant scalar curvature, namely, it is a Yamabe metric. We also show that the quadratic decay at infinity of the Ricci curvature of …

In a previous paper, the authors showed that metrics which are asymptotic to Anti-de Sitter-Schwarzschild metrics with positive mass admit a unique foliation by stable spheres with constant mean curvature. In this paper we extend that result to all asymptotically hyperbolic metrics for which the trace of the mass term …

Proves existence and compactness of solutions to $σ_2$-Nirenberg problem on sphere.

This paper is devoted to the existence of contact forms of prescribed Webster scalar curvature on a $3-$dimensional CR compact manifold locally conformally CR equivalent to the unit sphere $\mathbb{S}^{3}$ of $\mathbb{C}^{2}$. Due to Kazdan-Warner type obstructions, conditions on the function $H$ to be realized as a We…

The paper proves quasi-Einstein structures on manifolds admit Killing vector fields and provides new examples.

For a closed smooth manifold $M$ admitting a symplectic structure, we define a smooth topological invariant $Z(M)$ using almost-Kähler metrics, i.e. Riemannian metrics compatible with symplectic structures. We also introduce $Z(M, [[ω]])$ depending on symplectic deformation equivalence class $[[ω]]$. We first prove tha…

Sharp inequalities and extremals on compact Riemann surfaces with boundary.

The study examines metrics with unit volume or area on manifolds with boundaries, finding critical points and solving curvature problems.

The sigma invariant is studied for torus, K3 surface, and 3d manifolds.

This paper discovers new identities linking geodesic and orthogeodesic lengths on hyperbolic surfaces.

Establishes a correspondence between two mathematical identities.

Quandle identities give rise to subcomplexes in homology.

Einstein's philosophy uses differential identities to derive GR field equations.

The paper derives curvature identities for 5D and 6D Einstein manifolds.

Global Pestov identity proved on frame bundle and related fibrations.

RLINK uses deep reinforcement learning to improve user identity linkage across social networks.

Proves Bochner's identity on graphs using a new auxiliary graph.

Doodles link to commutator identities in a 2-sphere.