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### About Geometric Analysis

Geometric Analysis is a field of Pure Mathematics that lies in the interplay between Geometry and PDEs
and has applications to several branches of Mathematics such as Riemannian Geometry, Topology,
and Complex Variables, as well to General Relativity, Crystallography, Material Science, Architecture, and other fields.
Among many other achievements, the solutions of the Positive Mass Conjecture in General Relativity,
the Poincaré Conjecture in Topology, the Lawson, Willmore and Yau Conjectures in Differential Geometry,
or the Kobayashi Conjecture in Complex Geometry show the current relevance and usefulness of Geometric Analysis
in Pure Mathematics. Numerous well-established groups work in this field in several countries, which makes this topic highly-competitive.

### About our current research project

The project *Geometric Analysis* is supported by the
Ministerio de Ciencia e Innovación
(PID2020-117868GB-I00, September 1, 2021 — August 31, 2024) and their principal investigators are
Joaquín Pérez and
Antonio Alarcón at the University of Granada. Our *research team* is composed by 8 researchers in different areas of Geometric Analysis working in different centers in Spain. As for the *work team*, we count on two Ph.D. students, a young researcher, and two senior researchers from abroad.

The broad goal of this project is to delve into the understanding of several problems in Geometric Analysis, some in which we have extensive previous experience and some other fairly new problems with which we are trying to enlarge our research lines. We are focused on six subjects that are linked by strong synergies:

A) Minimal surfaces in Euclidean spaces.

B) Constant mean curvature and prescribed mean curvature surfaces.

C) Complex geometry.

D) Geometric flows.

E) PDE related problems.

F) Minimal surfaces in architecture.

### About our previous research projects

This research project *Geometric Analysis* continues a series of projects, with the same title, which have been successively supported by different calls of the Spanish research program. The composition of our team has been slightly changing in each edition of the project. The principal investigator (PI) of the first research project *Geometric Analysis* was
Antonio Ros (MTM2007-61775 from 2007 to 2012). The next PI was Joaquín Pérez (MTM2011-22547 from 2012 to 2014 and
MTM2014-52368-P from 2015 to 2018). Antonio Alarcón was incorporated as second PI of the project for its latest edition (MTM2017-89677-P from 2018 to 2021).