TY - CHAP
T1 - Applications of Min–Max Methods to Geometry
AU - Marques, Fernando C.
AU - Neves, André
N1 - Publisher Copyright:
© 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.
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 -