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Rigidity conjecture for equality in the 1-Bakry–Émery inequality on RCD spaces
Splitting conjecture. The existence of a non-constant function attaining equality in the 1-Bakry–Émery inequality should imply the splitting theorem.
Conjectureopenbakry-emery-inequality rcd-spaces splitting-theoremsarXiv posted 2 days ago

Rigidity conjecture for equality in the 1-Bakry–Émery inequality on RCD spaces