2 problems

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Interior angle sum conjecture for horizontal-like geodesic triangles in Sol geometry
Interior angle sum conjecture. The sum of the interior angles of any horizontal-like geodesic triangle is greater than $\pi$ :
Conjectureopengeodesic-geometry sol-geometry triangle-geometryarXiv posted 2 days ago
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Existence and uniqueness conjecture for constant mean curvature spheres in Sol_3
Let $\mathrm{Sol}_3$ be the three-dimensional Sol geometry, and let $H>0$ . A constant mean curvature (CMC) $H$ sphere is an immersed sphere in $\mathrm{Sol}_3$ with constant mean c…
Conjectureopenconstant-mean-curvature-surfaces isoperimetric-problem sol-geometryarXiv posted 2 days ago

Interior angle sum conjecture for horizontal-like geodesic triangles in Sol geometry