Harmonic Map Reading Seminar

Organizational meeting and introduction (Zhihan, April 15). Notes. Video.

Regularity theory of minimizing harmonic map (Anna, May 2). Notes. Video.

Regularity theory of minimizing harmonic map (Anna, May 9). Notes. Video.

Regularity theory of weak and stationary harmonic map (Sanghoon, May 24). Notes. Video.

Regularity theory of weak and stationary harmonic map (Sanghoon, May 29). Notes. Video.

Blow up analysis of stationary harmonic maps (Aditya, June 07). Notes. Video.

Harmonic map heat flow into NPC manifolds (Ben, June 21). Notes. Video.

Bubbling analysis for 2D harmonic maps and heat flows (Dongyeong, July 05). Notes. Video.

Bubbling analysis for 2D harmonic maps and heat flows (Dongyeong, July 12). Notes. Video.

Partial regularity of harmonic map heat flow in higher dimensions (Letian, July 19). Notes. Video.

Blow up analysis of harmonic map heat flow (Yangyang, July 26). Notes. Video.

Blow up analysis of harmonic map heat flow (Yangyang, Aug 02). Notes. Video.

Dynamics of defect measure of harmonic map heat flow (Zhihan, Aug 09). Notes. Video.

Energy Quantization of harmonic map heat flow (Zhihan, Aug 16). Notes. Video.

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Karpukhin, M., Nadirashvili, N., Penskoi, A. V., & Polterovich, I. (2021). An isoperimetric inequality for Laplace eigenvalues on the sphere. Journal of Differential Geometry, 118(2), 313-333.

Karpukhin, M. (2021). Index of minimal spheres and isoperimetric eigenvalue inequalities. Inventiones mathematicae, 223(1), 335-377.

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Naber, A., & Valtorta, D. (2017). Rectifiable-Reifenberg and the regularity of stationary and minimizing harmonic maps. Annals of Mathematics, 185(1), 131-227.

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