### Abstract

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 language | English (US) |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer |

Pages | 41-77 |

Number of pages | 37 |

DOIs | |

State | Published - 2020 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2263 |

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. https://doi.org/10.1007/978-3-030-53725-8_2