Videos

Introductory Workshop: New Frontiers in Curvature: Minimal surfaces II

Presenter
August 30, 2024
SLMath
Keywords:
  • mean curvature flow
  • Ricci flow
  • fully nonlinear flows
  • general relativity
  • mass
  • Ricci curvature
  • scalar curvature
  • sectional curvature
  • symmetry
  • Riemannian geometry
  • group actions
  • minimal surfaces
MSC:
  • 35J47 - Second-order elliptic systems
  • 35K40 - Second-order parabolic systems
  • 49J35 - Existence of solutions for minimax problems
  • 49Q05 - Minimal surfaces and optimization [See also 53A10
  • 58E12]
  • 53A10 - Minimal surfaces in differential geometry
  • surfaces with prescribed mean curvature [See also 49Q05
  • 49Q10
  • 53C42]
  • 53C20 - Global Riemannian geometry
  • including pinching [See also 31C12
  • 58B20]
  • 53C21 - Methods of global Riemannian geometry
  • including PDE methods
  • curvature restrictions [See also 58J60]
  • 53C22 - Geodesics in global differential geometry [See also 58E10]
  • 53C23 - Global geometric and topological methods (à la Gromov)
  • differential geometric analysis on metric spaces
  • 53C30 - Differential geometry of homogeneous manifolds [See also 14M15
  • 14M17
  • 32M10
  • 57T15]
  • 53C43 - Differential geometric aspects of harmonic maps [See also 58E20]
  • 53C50 - Global differential geometry of Lorentz manifolds
  • manifolds with indefinite metrics
  • 53E20 - Ricci flows
  • 58C40 - Spectral theory
  • eigenvalue problems on manifolds
  • 58D19 - Group actions and symmetry properties
  • 58E05 - Abstract critical point theory (Morse theory
  • Lyusternik-Shnirel'man theory
  • etc.) in infinite-dimensional spaces
  • 58E15 - Variational problems concerning extremal problems in several variables
  • Yang-Mills functionals [See also 81T13]
  • etc.
  • 58J35 - Heat and other parabolic equation methods for PDEs on manifolds
  • 83C05 - Einstein's equations (general structure
  • canonical formalism
  • Cauchy problems)
  • 83C15 - Exact solutions to problems in general relativity and gravitational theory
  • 83C20 - Classes of solutions
  • algebraically special solutions
  • metrics with symmetries for problems in general relativity and gravitational theory
  • 83C57 - Black holes
  • 83C60 - Spinor and twistor methods in general relativity and gravitational theory
  • Newman-Penrose formalism
  • 83C75 - Space-time singularities
  • cosmic censorship
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Abstract
I will review the basic principles regarding the basic techniques to prove existence of closed minimal hypesurfaces. I will talk about some current state of the art and finish by pointing out some possible new direction.