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math.AP2025
Optimal quantitative stability estimates for Alexandrov's Soap Bubble Theorem via Gagliardo-Nirenberg-type interpolation inequalities
João Gonçalves da Silva, Giorgio Poggesi
The paper provides optimal quantitative stability estimates for the celebrated Alexandrov's Soap Bubble Theorem within the class of domains, for any and $0 < α\…
math.AP2025
Fractional De Giorgi conjecture in dimension 2 via complex-plane methods
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
We provide a new proof of the fractional version of the De Giorgi conjecture for the Allen-Cahn equation in for the full range of exponents. Our proof combines a met…