
## 5. Eigenvalue Estimates

1. #### Problem 5.1.

[A. Fraser] Is there a flow related to Skeklov eigenvalue maximization? For closed surfaces in $S^3$, does Mean Curvature Flow improve $\lambda_1 \cdot Area$? What about balanced flow that keeps the center of mass?
• #### Problem 5.2.

[A. Fraser] Existence of high genus free boundary minimal surface in $B^3$.
• #### Problem 5.3.

[A. Fraser] Is the catenoid the only embedded free boundary minimal annulus in $B^3$ ?

Cite this as: AimPL: Geometric flows and Riemannian geometry, available at http://aimpl.org/flowriemannian.