学术报告（李楠 2025.11.25）

摘要：Naber proposed a conjecture which says that when a sequence of n-dimensional non-collapsed manifolds M_i Gromov-Hausdorff converges to X with uniform lower curvature bound, as a measure, the scalar curvature scal dvol_{g_i} converges to a locally finite measureμ = R dHⁿ + Φ dHⁿ⁻¹ + θ dHⁿ⁻² on X. We will show that the integral of the scalar curvature on the smooth part of an Alexandrov space is locally finite and this affirms Naber's conjecture for the smooth part R dHⁿ. We will also discuss the relation between this result and a conjecture by Gromov.