Rupert L. Frank

activity

20232026

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math.AP2026

The double sphere solution in the liquid drop model

Manuel del Pino, Rupert L. Frank, Monica Musso

We consider the problem of finding critical domains $Ω \subset R^{3}$ for the energy functional $$ \mathcal E (Ω) = {\rm Per}\,(Ω) + \frac 12 \iint_{Ω\times Ω} \frac{dx\,dy}{…

math.AP2026

Stability for the Affine Sobolev Inequality and its Critical Points for $p \geq 2$

Rupert L. Frank, Yinqin Li, Dachun Yang

We prove stability for the affine Sobolev inequality for exponents $p \geq 2$ with best possible norm and best possible stability exponent. We also show a corresponding result for c…

math.AP2026

From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near $T_{c}$ in the Non-Magnetic Case

Rupert L. Frank, Christian Hainzl, Dong Hao Ou Yang

We study the relation between the Bogoliubov-de Gennes (BdG) equation and the Ginzburg-Landau (GL) equation for a BCS model without external fields. While previous rigorous derivat…

The double sphere solution in the liquid drop model

Stability for the Affine Sobolev Inequality and its Critical Points for p≥2

From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near Tc​ in the Non-Magnetic Case

Stability for the Affine Sobolev Inequality and its Critical Points for $p \geq 2$

From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near $T_{c}$ in the Non-Magnetic Case