Related papers: Scalar-mean rigidity beyond warped product spaces

We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman…

We prove the general sharp mean value inequality for non-negative superharmonic functions and its corresponding rigidity, which removes the radius restriction of Schoen-Yau's classical result about this inequality. And we obtain an explicit…

We establish a rigidity theorem for Brendle and Hung's recent systolic inequality, which involves Gromov's notion of \(T^{\rtimes}\)-stabilized scalar curvature. Our primary technique is the construction of foliations by free boundary…

In this paper, we look for properties of gradient Yamabe solitons on top of warped product manifolds. Utilizing the maximum principle, we find lower bound estimates for both the potential function of the soliton and the scalar curvature of…

In this paper, we introduce and study the concept of \textit{Clairaut Riemannian warped product submersions} between Riemannian warped product manifolds. By generalizing the notion of Clairaut Riemannian submersions to the setting of…

Let M,g a compact Riemannian n-dimensional manifold. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. Also,…

We generalize Llarull's scalar curvature comparison to Riemannian manifolds admitting metric connections with parallel and alternating torsion and having a nonnegative curvature operator on 2-vectors. As a byproduct, we show that Euler…

We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a…

For a Kahler metric, the Riemannian scalar curvature is equal to twice the Chern scalar curvature. The question we address here is whether this equivalence can hold for a non-Kahler Hermitian metric. For such metrics, if they exist, the…

In this paper, we prove that a Riemannian $n$-manifold $M$ with sectional curvature bounded above by $1$ that contains a minimal $2$-sphere of area $4\pi$ which has index at least $n-2$ has constant sectional curvature $1$. The proof uses…

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic…

We consider the problem of finding a metric in a given conformal class with prescribed nonpositive scalar curvature and nonpositive boundary mean curvature on a compact manifold with boundary, and establish a necessary and sufficient…

A Dirac-type operator on a complete Riemannian manifold is of Callias-type if its square is a Schr\"{o}dinger-type operator with a potential uniformly positive outside of a compact set. We develop the theory of Callias-type operators…

The Schouten tensor \ $A$ \ of a Riemannian manifold \ $(M,g)$ provides important scalar curvature invariants $\sigma_k$, that are the symmetric functions on the eigenvalues of $A$, where, in particular, $\sigma_1$ \ coincides with the…

In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between algebraic or analytic properties of the…

In this article we study the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary. We prove that for such manifolds of certain dimensions, those spaces are not connected and have nontrivial fundamental…

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give…

Let $(M, \bar g)$ be an $n$-dimensional complete Riemannian manifold. In this paper, we considers the following conformal scalar curvature rigidity problem: Given a compact smooth domain $\Omega$ with $\partial \Omega$, can one find a…

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…