Our research, which started 25 years ago within the field of the geometry of submanifolds, is being addressed in the most recent years towards the applications of the modern techniques of geometric and convex analysis to the study of certain global problems, both in the field of differential geometry and in the field of convex geometry, as well as in the interplay of both topics. It is in this context where this research project must be placed, with the main aim of going on making progress in the study and the deep knowledge of different problems in differential and convex geometry by means of the application of the most advanced techniques in analysis and geometry, and with the decided purpose of not only keeping but increasing, both quantitatively and qualitatively, the scientific production of our group, which has experienced a remarkable growth in recent years.

As explained in the technical report, the research activity programme presented in this project is a natural continuation of what has been developed by our group in the last decade. Its interest and attraction is supported by the relevance of publications, the financing of projects in competitive calls and positive assessment by expert committees. In this research project we keep on considering and addressing open problems of great significance that arise naturally either from our own results or others that, coming from other groups, are of interest to a significant part of the international community. The relevance and specific innovation and novelty of this research programme lie essentially in the possibility of enjoying a stable and long term financial support which will allow us to keep our commitment of excellence.

Research Objectives

1. To continue growing up in the impact of our research publications and increasing the quality of our research activity and the international presence of our research.
2. To diversify our research activity in two different ways, opening new lines of research which allow us to secure our leadership at national and international levels, and collaborating with other groups, which improve the international visibility of our group.
3. To incorporate outstanding researchers to our group through medium length research stays or through postdoctoral research contracts of longer duration.
4. To consolidate our research group as a group of international recognition in the fields of differential and convex geometry and as a reference group in the national scene. To improve the international visibility of our group.
5. To increase the availability of the results of our research, both from within and from outside Mathematics, and to publicize our research activity, not only in our university but also in other institutions, including scientists and technologists from other disciplines.