Daniel Ballesteros-Chávez
Asystent / Assistant
Wydział Automatyki, Robotyki i Elektrotechniki / Faculty of Control, Robotics & Electrical Engineering
Instytut Matematyki / Institute of Mathematics
Politechnika Poznańska / Poznan University of Technology
email: daniel.ballesteroschavez@put.poznan.pl
github: http://github.com/ennaniux

My research is on elliptic partial differential equations of fully nonlinear type that appear in geometric problems, for instance, prescribed curvature. A classical problem of this type is the Minkowski problem which is strongly related to the Monge-Ampère equation. I am also interested in the geometry of hypersurfaces in both Riemannian and semi-Riemannian manifolds. These equations are usually represented as symmetric functions on the eigenvalues of the second fundamental form of the hypersurface with respect to the induced metric. Then we can study the properties of the prescription function to ensure the existence of such a hypersurface.

• Weyl estimates for spacelike hypersurfaces in de Sitter space with W. Klingenberg and B. Lambert. Pacific Journal of Mathematics. arXiv, 2021.

• Prescribed k-symmetric curvature hypersurfaces in de Sitter space with W. Klingenberg and B. Lambert. Canadian Mathematical Bulletin. arXiv, 2019.

• Curvature Estimates Of Spacelike Surfaces In De Sitter Space. arXiv, 2019.

• Existence of Classical Solutions of Second Order Partial Differential Equations. (still in progress)
• Notes: Introduction to Complex Analysis (html)
• Notes: Introduction to Differential Geometry (html)
• Notes: Worked examples on complex numbers and linear algebra

• Calculus on Several Variables. Matematyka 2020/2021-I-4. Notes in moodle.

• Introduction to Complex Analysis. Matematyka 2020/2021-I-4. Notes in moodle.

• Modelling with R. Informatyka 2021/2022-I-5. Notes in moodle. A catalogue of Models in R.

• "On the Isometric embeddings of spheres into de Sitter space". Spanish-Polish Mathematical Meeting. RSME-SEMA-SCM-PTM. Łódź, Poland. Sep 2023.

• "On the Weyl problem in de Sitter space and a Weyl-type estimate". Geometry and Differential Equations Seminar. Institute of Mathematics of the Polish Academy of Science. Warsaw, Poland. Oct 2022.

• "On the prescribed curvature problem for starshaped hypersurfaces". Workshop Modern Techniques in Riemannian Geometry. Faculty of Sciences UNAM, Mexico & Durham University, UK. Apr 2021.

• "A curvature estimate for hypersurfaces in de Sitter space". Faculty of Applied Mathematics Seminar. Silesian University of Technology, Gliwice, Poland. Mar 2021.

• "A \(C^2\) estimate for the prescribed curvature problem in de Sitter space". Geometry and Differential Equations Seminar. Institute of Mathematics of the Polish Academy of Science. Warsaw, Poland. Dec 2019.

• "Nirenberg's solution of the Weyl problem". Geometry and Topology Seminar. Durham University. Dec 2019.

• "A \(C^2\) estimate for the prescribed curvature problem in de Sitter space". Differential Geometry and Analysis Seminar. Marburg University, Germany. Jul 2019.

• Poster. "Curvature estimates for prescribed curvature equation of hypersurfaces in de Sitter space". Arbeitstagung on Geometry. Max Planck Institute for Mathematics. Bonn, Germany. Jul 2019.

• Poster. "Dirichlet Problem for Prescribed Curvature in Hyperbolic Space (revisited)". International Conference of Mathematical Sciences (ICMS). Maltepe Univeristy, Istanbul. Aug 2018.

• "Sobre el problema no lineal de k-curvatura prescrita en hipersuperficies del espacio hiperbólico y de Sitter". Mexican Mathematicians in the World. Casa Matemática Oaxaca. Oaxaca, Mex. Jun 2018.

• "Prescribed k-curvature of convex closed hypersurfaces in \(H^n\) and \(S^n\) : a fully nonlinear elliptic problem".Yorkshire and Durham Geometry Days. Durham University. Durham, UK. Mar 2018.

• "Fully nonlinear PDE on the sphere from prescribed curvature problem in hyperbolic space". British Mathematical Colloquium. Durham, UK. Apr 2017.

• Poster. "Dirichlet Problem for Prescribed Curvature in Hyperbolic Space". LMS-CMI Research School. Reading University. REading, UK. Jul 2016.

• "On the Minkowski Problem in Hyperbolic Space". 9th European Conference on Elliptic and Parabolic Problems. Insitut für Mathematik Universität Zürich. Gaeta, Italy. May 2016.

• Poster. "Prescribing Homogeneous Curvatures in Hyperbolic Space". Winter School 2016 on Geometric Evolution Equations. Regensburg University. Regensburg, Germany. Feb 2016.

• "On the Existence of Convex Surfaces with Prescribed k-symmetric Curvatures". Geometry and Topology seminar. Durham University. Nov 2015.

• "El Laplaciano como ejeplo de Operador Elíptico". Seminario de Becarios. IMATE-UNAM. Mexico City. May 2012.

Aya oppatihua nican.
Ayac ichan in tlalticpac, oo,
in ayoppa-tihua in tlalticpac in.
Zan nicuicanitl, Ayaho, on nichoca
ye ni quilnamiqui Nezahualcoyotl. Ayyo.