Variational Methods in Geometry
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- Struwe, M. Jahresber. Dtsch. Math. Ver. (2017) 119: 71. doi:10.1365/s13291-016-0155-0
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Variational principles are ubiquitous in nature. Many geometric objects such as geodesics or minimal surfaces allow variational characterizations. We recall some basic ideas in the calculus of variations, also relevant for some of the most advanced research in the field today, and show how a subtle variation of standard methods can lead to surprising improvements, with numerous applications.