2 problems

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The radial-density hypersphere conjecture in Euclidean space
Radial-density hypersphere conjecture. In $\mathbb{R}^{n}$ with density $r^{p}$ , hyperspheres through the origin are uniquely isoperimetric.
Conjectureopenisoperimetric-geometry manifolds-with-density radial-densityarXiv posted 2 days ago
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The plane radial-density conjecture for circles, undularies, and pinched circles
Plane radial-density conjecture. For $k\in[0,\infty)$ , the following curves are isoperimetric:
Conjectureopenisoperimetric-geometry manifolds-with-density radial-densityarXiv posted 2 days ago

The radial-density hypersphere conjecture in Euclidean space