Simone Calamai

On the Chern–Yamabe problem

We initiate the study of an analogue of the Yamabe problem for complex manifolds. More precisely, fixed a conformal Hermitian structure on a compact complex manifold, we are concerned in the existence of metrics with constant Chern scalar curvature. In this note, we set the problem and we provide a positive answer when the expected constant Chern scalar curvature is non-positive. In particular, this includes the case when the Kodaira dimension of the manifold is non-negative. Finally, we give some remarks on the positive curvature case, showing existence in some special cases and the failure, in general, of uniqueness of the solution.

A vanishing result for strictly p-convex domains

In view of Andreotti and Grauert (Bull Soc Math France 90:193–259, 1962) vanishing theorem for

Cohomologies of Generalized Complex Manifolds and Nilmanifolds

q

On minimal Legendrian submanifolds of Sasaki–Einstein manifolds

-complete domains in

Toric extremal Kähler-Ricci solitons are kähler-Einstein

\mathbb C ^{n}

The Dirichlet and the weighted metrics for the space of Kähler metrics

, we reprove a vanishing result by Sha (Invent Math 83(3):437–447, 1986), and Wu (Indiana Univ Math J 36(3):525–548, 1987), for the de Rham cohomology of strictly