Glued spaces and lower Ricci curvature bounds
Abstract
Abstract We consider Riemannian manifolds $$M_i$$ M i , $${i=0,1}$$ i = 0 , 1 , with boundary and $$\Phi _i\in C^{\infty }(M_i)$$ Φ i ∈ C ∞ ( M i ) non-negative such that $$(M_i, \Phi _i)$$ ( M i , Φ i ) has Bakry-Emery N -Ricci curvature bounded from below by K . Let $$Y_0$$ Y 0 and $$Y_1$$ Y 1 be isometric, compact components of the boundary of $$M_0$$ M 0 and $$M_1$$ M 1 respectively and assume $$\Phi _0=\Phi _1$$ Φ 0 = Φ 1 on $$Y_0\simeq Y_1$$ Y 0 ≃ Y 1 . We assume that $$\Pi _0+\Pi _1=:\Pi \ge 0$$ Π 0 + Π 1 = : Π ≥ 0 (*), and $$d\Phi _0(\nu _0)+ d\Phi _1(\nu _1)\le {{\,\textrm{tr}\,}}\Pi $$ d Φ 0 ( ν 0 ) + d Φ 1
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Point processes and geometric inequalities
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 5
- Publication date
- 21 April 2026
- Language
- EN