Advances in Geometry

ADVANCES IN GEOMETRY

MANAGING EDITORS Theo Grundhöfer, Würzburg William M. Kantor, Eugene Michael Joswig, Berlin Gábor Korchmáros, Potenza Alexander Kreuzer, Hamburg EDITORIAL BOARD Jeffrey C. Lagarias, Ann Arbor John Bamberg, Crawley Thomas Leistner, Adelaide Eiichi Bannai, Shanghai Rainer Löwen, Braunschweig Renzo Cavalieri, Fort Collins Kaoru Ono, Kyoto Izzet Coskun, Chicago John G. Ratcliffe, Nashville Frank Duzaar, Erlangen Claus Scheiderer, Konstanz Patrick Eberlein, Chapel Hill Hendrik Van Maldeghem, Gent Graziano Gentili, Florence Steven H. Weintraub, Bethlehem Martin Henk, Berlin Richard Weiss, Medford ADVANCES IN GEOMETRY is a mathematical journal for the publication of original research articles of excellent quality in the broad area of geometry.

All information regarding notes for contributors, subscriptions, Open access, back volumes and orders is available online at www.degruyter.com/advgeom.

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ISSN 1615-715X · e-ISSN 1615-7168 · CODEN AGDEA3

RESPONSIBLE EDITORS Theo Grundhöfer, Institut für Mathematik, Universität Würzburg, Emil-Fischer-Str. 30, 97074 Würzburg, Germany. Email: [email protected] Michael Joswig, Institut für Mathematik, Technische Universität Berlin, Sekretariat MA 6-2, Straße des 17. Juni 136, 10623 Berlin, Germany. Email: [email protected]

JOURNAL MANAGER Theresa Haney, De Gruyter, Genthiner Straße 13, 10785 Berlin, Germany. Tel.: +49 (0)30 260 05-375, Fax: +49 (0)30 260 05-250 Email: [email protected]

RESPONSIBLE FOR ADVERTISEMENTS Claudia Neumann, De Gruyter, Genthiner Straße 13, 10785 Berlin, Germany. Tel.: +49 (0)30 260 05-226, Fax: +49 (0)30 260 05-264 Email: [email protected]

PRINTING Franz X. Stückle Druck und Verlag e.K., Ettenheim Adv. Geom. 2019 | Volume 19 | Issue 3

Contents

Sergey Stepanov and Irina Tsyganokr Ulrich Dempwolff A remark on the mixed scalar curvature of a manifold Doubly transitive dimensional dual hyperovals: with two orthogonal totally umbilical distributions universal covers and non-bilinear examples 359 291 Indranil Biswas, Ugo Bruzzo and Sudarshan Gurjar Jiaqi Hu, Ge Xiong and Du Zou Higgs bundles and fundamental group chemes 381

On mixed Lp John ellipsoids 297 P. Benedini Riul and R. Oset Sinha Semyon Alesker A relation between the curvature ellipse and the Valuations on convex functions and convex sets curvature parabola 389 and Monge–Ampère operators 313 Leonardo Bagaglini

Miriam Abdón, Herivelto Borges and Luciane Quoos Non-orientable three-submanifolds of G2-manifolds Weierstrass points on Kummer extensions 323 401

Bart Dioos and Joeri Van der Veken Moritz Gruber The Bonnet problem for harmonic maps to the The growth of the first non-Euclidean filling volume three-sphere 335 function of the quaternionic Heisenberg group 415

Mustafa Gezek, Vladimir D. Tonchev and Tim Wagner Paul Baird and Elsa Ghandour Maximal arcs in projective planes of order 16 and A class of analytic pairs of conjugate functions in related designs 345 dimension three 421

Ivan Bazhov On the decomposition of the small diagonal of a K3 surface 353