arXiv subjects
Publications and source records attributed to Rondinelle Batista.
The purpose of this article is study rigidity of free boundary minimal two-disks that locally maximize the modified Hawking mass on a Riemannian three-manifold with positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of Σ, we prove that a neighborhood of it in M is isometric to one of the half de Sitter-Schwarzschild space.
We provide a harmonic level set proof of the positive mass theorem for asymptotically flat $3$-manifolds with a non-compact boundary first established by Almaraz-Barbosa-de Lima.
The purpose of this article is to prove that, under suitable constrains on the electrovacuum spacetime $M$, if $Σ\subset M$ is an embedded strictly stable minimal two-sphere which locally maximizes the charged Hawking mass, then there exist a neighborhood of it in $M$ isometric to the Reissner-Nordström-de Sitter space. At the same time, motived by \cite{Brendle}, we will deduce an estimate for area of a two-sphere which is locally area minimizing in an electrovacuum spacetime. Moreover, if the equality holds, then there exist a neighborhood of it in $M$ isometric to the charged Nariai space.
The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\big(M^n,\,g,\,X,\,λ\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\Bbb{S}^{n}$. As a consequence we obtain that every compact non-trivial almost Ricci soliton with constant scalar curvature is gradient. Moreover, the vector field $X$ decomposes as the sum of a Killing vector field $Y$ and the gradient of a suitable function.