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)|
|Title of host publication||Lecture Notes in Mathematics|
|Number of pages||37|
|State||Published - 2020|
|Name||Lecture Notes in Mathematics|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory