Applications of Min–Max Methods to Geometry

Fernando C. Marques, André Neves

Research output: Chapter in Book/Report/Conference proceedingChapter


The existence of minimal surfaces in closed manifolds is a classical subject with a long history. This chapter presents some recent advances on the subject, motivated by Yau’s conjecture concerning the existence of infinitely-many ones. The main tools used here are a combination of techniques from Geometric Measure Theory and Minimal methods. The conjecture is proved for a large class of metrics and, via the concept of volume spectrum, a density result is also derived.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
Number of pages37
StatePublished - 2020

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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  • Cite this

    Marques, F. C., & Neves, A. (2020). Applications of Min–Max Methods to Geometry. In Lecture Notes in Mathematics (pp. 41-77). (Lecture Notes in Mathematics; Vol. 2263). Springer.