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Issue no. 1 Table of Contents

The flatness of the 𝒪-module of smooth functions and integral representation
Mats Andersson
Existence and uniqueness of S 1 -invariant Kähler–Ricci solitons
Johannes Schäfer
Irrational pencils and Betti numbers
Francisco Nicolás; Pierre Py
About relative polar varieties and Brasselet numbers
Hellen Santana
On stability of rotational 2D binary Bose–Einstein condensates
Rémi Carles; Van Duong Dinh; Hichem Hajaiej
Sobolev’s inequality under a curvature-dimension condition
Louis Dupaigne; Ivan Gentil; Simon Zugmeyer
Proper superminimal surfaces of given conformal types in the hyperbolic four-space
Franc Forstnerič
Remark on an inequality for closed hypersurfaces in complete manifolds with nonnegative Ricci curvature
Xiaodong Wang
Minimal hypersurfaces and geometric inequalities
Simon Brendle