6 papers
On a Variant of the Penrose Conjecture
Sven Hirsch, Yipeng Wang
We give a counterexample to a recently conjectured variant of the Penrose inequality.
Area-minimizing capillary cones
Benjy Firester, Raphael Tsiamis, Yipeng Wang
We construct non-flat minimal capillary cones with bi-orthogonal symmetry groups for any dimension and contact angle. These cones interpolate between rescalings of a singular solut…
Stability inequalities for one-phase cones
Benjy Firester, Raphael Tsiamis, Yipeng Wang
We obtain strict stability inequalities for homogeneous solutions of the one-phase Bernoulli problem. We prove that in dimension and above, cohomogeneity one solutions with bi-…
On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldán
Simon Brendle, Raphael Tsiamis, Yipeng Wang
We consider fill-ins of spin manifolds with scalar curvature bounded by . Gromov proposed a conjecture relating the infimum of the mean curvature of such a fill-in to the…
Uniqueness of Cylindrical Tangent Cones
Benjy Firester, Raphael Tsiamis, Yipeng Wang
We show the uniqueness of the cylindrical tangent cone for area-minimizing hypersurfaces in , completing the u…
On Gromov's rigidity theorem for polytopes with acute angles
S. Brendle, Y. Wang
In his ``Four Lectures", Gromov conjectured a scalar curvature extremality property of convex polytopes. Moreover, Gromov outlined a proof of the conjecture in the special case whe…