Energy identity for stationary harmonic maps

Abstract: We present the proof for Energy Identity for stationary harmonic maps. In particular, given a sequence of stationary harmonic maps weakly converging to a limit with a defect measure for the energy, then $m-2$ almost everywhere on the support of this measure the density is the sum of energy of bubbles. This is equivalent to saying that annular regions (or neck regions) do not contribute to the energy of the limit.

This result is obtained via a quantitative analysis of the energy in annular regions for a fixed stationary harmonic map. The proof is technically involved, but it will be presented in simplified cases to try and convey the main ideas behind it. (Preprint available on arXiv:2401.02242)

analysis of PDEsdifferential geometry

Audience: researchers in the topic

( paper )

---

NCTS international Geometric Measure Theory seminar

Series comments: We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences.

Focus: regularity and singularity theories for submanifolds of Riemannian manifolds and some of its applications.

Frequency: one presentation every other month.

Registration: required for new participants, go to the seminar website (allow at least one working day for processing).

Virtual venue: HyHyve space NCTS iGMT seminar (only for registered participants, opened one hour before the events).

You might want to consult the description of the premises and instructions.

Former organiser: Guido De Philippis (till March 2022).

---