Abstract We prove the macroscopic cousins of three conjectures: (1) a conjectural bound simplicial volume Riemannian manifold in presence lower scalar curvature bound, (2) conjecture that rationally essential manifolds do not admit metrics positive curvature, (3) $$\ell ^2$$ ℓ 2 </...

In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and Witten, we prove the following theorem: For any compact manifold with boundary and nonnegative scalar curvature, if it is spin and its boundary can be isometrically embedded into Euclidean space as a stric...