# Presentations

The presentations will be held in the last two weeks of classes.

### Schedule

- Mon, Apr 17: Seongmin Jeon,
*Proof of “Filling holes” estimate* - Wed, Apr 19: Yuqing Li,
*Schaeffer’s example of singular points* - Fri, Apr 21: Zachary Selk,
*Andersson-Weiss counterexample* - Mon, Apr 24: Hengrong Du,
*Friedland-Hayman Inequality* - Wed, Apr 26: Ziyao Yu,
*Up to boundary *C*^{1,1}regularity* - Fri, Apr 28: Qinfeng Li,
*Uniqueness of blowups using Epiperimetric inequality*

### Topics for Presentations

- Proof of “Filling holes” estimate, [PSU, Lemma 9.1 and Exercise 9.3]
- Schaeffer’s example of singular points, [PSU, §7.3 and Exercise 7.2]
- Andersson-Weiss counterexample, [PSU, §2.5 and Exercise 2.8]
- Friedland-Hayman Inequality, from [CS, §12.3]
- Up to boundary
*C*^{1,1}regularity [PSU, §2.4] - Uniqueness of blowups using Epiperimetric inequality, [Wei, §6]

#### References

[CS] L. Caffarelli, S. Salsa, *A geometric approach to free boundary problems*, Graduate Studies in Mathematics 68, American Mathematical Society, Providence, RI, 2005

[PSU] A. Petrosyan, H. Shahgholian, N. Uraltseva, *Regularity of free boundaries in obstacle-type problems*, Graduate Studies in Mathematics 136, American Mathematical Society, Providence, RI, 2012

[Wei] G.S. Weiss, *A homogeneity improvement approach to the obstacle problem*, Invent. Math. 138 (1999), no. 1, 23–50