Search Our Scientific Publications & Authors

Ann Mat Pura Appl 2022 4;201(2):801-822. Epub 2021 Aug 4.

Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany.

We derive precise transformation formulas for synthetic lower Ricci bounds under time change. More precisely, for local Dirichlet forms we study how the curvature-dimension condition in the sense of Bakry-Émery will transform under time change. Similarly, for metric measure spaces we study how the curvature-dimension condition in the sense of Lott-Sturm-Villani will transform under time change. Read More

Ann Mat Pura Appl 2021 21;200(5):1935-1960. Epub 2021 Jan 21.

Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, De Uithof, 3584 CC Utrecht, The Netherlands.

Motivated by a Möbius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular Möbius invariant point-insertion-rule, comparable to the classical four-point-scheme, we construct circles along discrete curves. Asymptotic analysis shows that these circles defined on a sampled curve converge to the smooth curvature circles as the sampling density increases. Read More

Ann Mat Pura Appl 2021 12;200(6):2797-2827. 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