printable pdf
比利时vs摩洛哥足彩 ,
university of california san diego

****************************

special colloquium

nicos kapouleas

brown university

gluing constructions for minimal surfaces and other geometric objects

abstract:

during my talk i will concentrate on the current status and ongoing work on the following: 1) doubling constructions for minimal surfaces: i will first discuss the general motivation and framework and i will mention briefly the earlier work in [kapouleas-yang: 2010] and work of david wiygul. i will then concentrate on the ideas in [kapouleas: arxiv:1409.0226, 2014] and in particular i will present in some detail the linearized doubling methodology. i will also mention ongoing work and future possibilities. 2). desingularization constructions for minimal surfaces: i will first discuss the $o(2)$-invariant initial configuration case as in [kapouleas: jdg 1997]. i will then briefly discuss some recent constructions with more symmetry in various settings, including a current construction with martin li for free boundary minimal surfaces in the unit three-ball. i will outline and discuss extensions to less symmetric settings or settings without any symmetries as discussed in [kapouleas: clay proceedings, vol.2, 2005], [kapouleas: alm, vol 20, 2011], and further ongoing work. 3). i will discuss potential constructions for einstein four-manifolds and some related ancient solutions for the ricci flow as in [brendle-kapouleas: arxiv:1405.0056, 2014]. 4). finally to the extent that time permits i will briefly discuss gluing constructions for special lagrangian cones as in [haskins-kapouleas: inventiones 2007] and [haskins-kapouleas: alm, vol.7, 2008] and ongoing work, and also for cmc (hyper)surfaces in early work of mine and recent work with christine breiner [breiner-kapouleas: math. annalen 2014] and [breiner-kapouleas: preprint close to completion].

hosts: ben chow and lei ni

february 8, 2016

3:00 pm

ap&m 6402

****************************