TY - CHAP

T1 - Applications of Min–Max Methods to Geometry

AU - Marques, Fernando C.

AU - Neves, André

N1 - Funding Information:
The first author is partly supported by NSF-DMS-1811840. The second author is partly supported by NSF DMS-1710846 and by a Simons Investigator Grant.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-030-53725-8_2

DO - 10.1007/978-3-030-53725-8_2

M3 - Chapter

AN - SCOPUS:85090365241

T3 - Lecture Notes in Mathematics

SP - 41

EP - 77

BT - Lecture Notes in Mathematics

PB - Springer

ER -