We construct several new examples of homogeneous domains in complex space that do not have bounded realisations. They are equivalent to tubes over affinely homogeneous domains in real space and have a real-analytic everywhere Levi non-degenerate non-umbilic boundary. Using the geometry of the boundary, we determine the full automorphism groups of the domains. We also discuss some interesting ex...

It was recently shown by R. Souam and E. Toubiana [33] that the (non constantly curved) Berger spheres do not contain totally umbilic surfaces. Nevertheless in this article we show, by perturbative arguments, that all analytic metrics su ciently close to the round metric g0 on S possess generalized totally umbilic 2-spheres, namely critical points of the conformal Willmore functional ∫ Σ |A◦|2 ...

Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3 with boundary ∂M . We denote the Ricci curvature, scalar curvature, mean curvature, and the second fundamental form by Ric, R , h, and Lαβ , respectively. The Yamabe problem for manifolds with boundary is to find a conformal metric ĝ = eg such that the scalar curvature is constant and the mean curvature is zero. The boundary is call...

In this work we classify the singularities obtained from the Gibbs potential of a lattice gas model with three components, two order parameters, and five control parameters applying the general theorems provided by catastrophe theory. In particular, we clearly establish the existence of Landau potentials in two variables or, in other words, corank-2 canonical forms that are associated with the ...

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