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Ann Mat Pura Appl 2021 Apr 12:1-31. Epub 2021 Apr 12.

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240 People's Republic of China.

We consider a uniform -bundle on a complex rational homogeneous space and show that if is poly-uniform with respect to all the special families of lines and the rank is less than or equal to some number that depends only on , then is either a direct sum of line bundles or unstable with respect to some numerical class of a line. So we partially answer a problem posted by Muñoz et al. (Eur J Math 6:430-452, 2020). Read More

Ann Mat Pura Appl 2021 2;200(1):101-116. Epub 2020 May 2.

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

We consider here three-dimensional water flows governed by the geophysical water wave equations exhibiting full Coriolis and centripetal terms. More precisely, assuming a constant vorticity vector, we derive a family of explicit solutions, in Eulerian coordinates, to the above-mentioned equations and their boundary conditions. These solutions are the only ones under the assumption of constant vorticity. Read More

Ann Mat Pura Appl 2021 29;200(1):35-50. Epub 2020 Apr 29.

Institut für Diskrete Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.

This paper studies the boundary behaviour of -polyharmonic functions for the simple random walk operator on a regular tree, where is complex and , the -spectral radius of the random walk. In particular, subject to normalisation by spherical, resp. polyspherical functions, Dirichlet and Riquier problems at infinity are solved, and a non-tangential Fatou theorem is proved. Read More

Ann Mat Pura Appl 2020 20;199(5):2039-2059. Epub 2020 Feb 20.

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

In this article, we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that interpolates between the functionals for harmonic and biharmonic maps. In the case of a spherical target, we will derive a conservation law and use it to show the smoothness of weak solutions. Read More