## Farthest points on most Alexandrov surfaces

Published in Advances in Geometry

We study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where most is used in the sense of Baire categories.

Published in Advances in Geometry

We study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where most is used in the sense of Baire categories.

Published in Advances in Geometry

Masures are generalizations of Bruhat–Tits buildings and the main examples are associated with almost split Kac–Moody groups G over non-Archimedean local fields. In this case, G acts strongly transitively on its corresponding masure Δ as well as on the building at infinity of Δ, which is the twin building associated with G. The aim of this article ...

Published in Advances in Geometry

The invariant theory for conformal hypersurfaces is studied by treating these as the conformal infinity of a conformally compact manifold. Recently it has been shown how, given a conformal hypersurface embedding, a distinguished ambient metric is found (within its conformal class) by solving a singular version of the Yamabe problem [21]. This enabl...

Published in Advances in Geometry

This paper focuses on the classification (up to isomorphism) of all toric log Del Pezzo surfaces with exactly one singularity, and on the description of how they are embedded as intersections of finitely many quadrics into suitable projective spaces.

Published in Advances in Geometry

To study the splitting of nodal plane curves with respect to contact conics, we define the splitting type of such curves and show that it can be used as an invariant to distinguish the embedded topology of plane curves. We also give a criterion to determine the splitting type in terms of the configuration of the nodes and tangent points. As an appl...

Published in Advances in Geometry

We study a conjecture, due to Voisin, on 0-cycles on varieties with pg = 1. Using Kimura’s finite dimensional motives and recent results of Vial’s on the refined (Chow–)Künneth decomposition, we provide a general criterion for Calabi–Yau manifolds of dimension at most 5 to verify Voisin’s conjecture. We then check, using in most cases some cohomolo...

Published in Advances in Geometry

We give criteria for which a principal curvature becomes a bounded C∞-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended distance squared functions of wave fronts. Moreover, we relate these singularities to some geometric invariants of fr...

Published in Advances in Geometry

We classify rational, irreducible quartic symmetroids in projective 3-space. They are either singular along a line or a smooth conic section, or they have a triple point or a tacnode.

Published in Advances in Geometry

By [4] a doubly transitive, non-solvable dimensional dual hyperoval D is isomorphic either to the Mathieu dual hyperoval or to a quotient of a Huybrechts dual hyperoval. In order to determine all doubly transitive dimensional dual hyperovals, it remains to classify the solvable ones, and this paper is a contribution to this problem. A doubly transi...

Published in Advances in Geometry

The notion of a valuation on convex bodies is very classical; valuations on a class of functions have been introduced and studied by M. Ludwig and others. We study an explicit relation between continuous valuations on convex functions which are invariant under adding arbitrary linear functionals, and translation invariant continuous valuations on c...