2 problems

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Non-algebraic stationary surface conjecture at total curvature $4\pi$
Non-algebraic stationary surface conjecture. There does not exist any complete, non-algebraic stationary surface immersed in $\mathbb{R}^4_1$ with finite total Gaussian curvature
Conjectureopenlorentz-geometry stationary-surfaces total-curvaturearXiv posted 2 days ago
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The Vague Conjecture on global geometric flows and compact geometric manifolds
A conformal Lorentz structure on an $m+2$ -dimensional manifold is an $\mathrm{O}(m+1,1)\times {\mathbb R}^+$ -structure, and a conformally flat Lorentz structure is an integrable su…
Conjectureopenconformal-geometry geometric-structures lorentz-geometryarXiv posted 2 days ago

Non-algebraic stationary surface conjecture at total curvature 4π4\pi4π