Spherical cones: classification and a volume minimization principle

Tran-Trung Nghiem (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

Using a variational approach, we establish the equivalence between a weighted volume minimization principle and the existence of a conical Calabi-Yau structure on horospherical cones with mild singularities. This allows us to do explicit computations on the examples arising from rank-two symmetric spaces, showing the existence of many irregular horospherical cones.

Mots clés: 2020 Mathematics Subject Classification. 14M27; 32Q25; 32Q26; 35J96 Spherical cones; Conical Calabi-Yau metrics; Real Monge-Ampère equations; Variational approach; Weighted volume minimization

Domaines: Mathématiques [math]; Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Tran-Trung Nghiem. Spherical cones: classification and a volume minimization principle. 2022. ⟨hal-03863444⟩