Computed p-widths for hemisphere, first for manifolds with boundary.
problem Finding p-widths for manifolds with boundary.
method Computed p-widths for the hemisphere.
result First known p-widths for a manifold with boundary.
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12 results for “p-widths”
The p-widths of a polygonmath.DG
Polygon -widths are found via billiard trajectories.
problem Finding -widths of polygons.
method Proved via billiard trajectories and computed specific cases.
result Polygon -widths are achieved by billiard trajectories.
The p-widths of math.DG
Computed p-widths for real projective plane.
problem Calculating p-widths for real projective plane.
method Standard metric used to compute p-widths.
result Computed p-widths for real projective plane.
The isospectral problem for p-widths is solved using Zoll metrics on S^2.
problem Determine if a Riemannian manifold is uniquely determined by its p-widths.
method Construct counterexamples on S^2 using Zoll metrics and properties of geodesic p-widths.
result Many counterexamples exist on S^2, showing uniqueness is not guaranteed.
The p-widths of a surfacemath.DG
New insights into -widths of surfaces, proving optimality and calculating constants.
problem Understanding -widths of surfaces and their relationship to geodesics.
method Analyzing min-max sequences of minimal submanifolds and sweepouts of surfaces.
result Optimal sweepouts of the round two-sphere by great circles.
While studying the existence of closed geodesics and minimal hypersurfaces in compact manifolds, the concept of width was introduced in different contexts. Generally, the width is realized by the energy of the closed geodesics or the volume of minimal hypersurfaces, which are found by the Minimax argument. Recently, Ma…
On compact 2-manifolds with non-empty convex boundary, we prove a regularity result for integral 1-varifolds that are stationary with free boundary and -almost minimizing in small annuli. That regularity says that is a free boundary finite geodesic network. Next, using that regularity, we compute …
Study on geodesics proving index and intersection bounds, with examples of multiplicity.
problem Understanding the index and intersections of min-max geodesics on surfaces.
method Proof of tangent cone structure, construction of metrics with multiplicity.
result Upper bounds on index and intersections, examples of multiplicity.
Upper bound for Morse index of min-max varifolds.
problem Bounding Morse index of varifolds.
method Proving upper bound for Morse index of min-max stationary integral varifolds.
result Upper bound for Morse index of min-max stationary integral varifolds.
The paper solves min-max widths on a 3-sphere and strengthens multiplicity theorems.
problem Which min-max widths of the unit 3-sphere lie between and ?
method Homological min-max theory and stronger versions of multiplicity one theorems.
result Proves the 10th to 13th min-max widths of the unit 3-sphere lie between and .
We show that on a compact Riemmanian manifold , nodal sets of linear combinations of any smooth functions form an admissible sweepout provided these linear combinations have uniformly bounded vanishing order. This applies in particular to finite linear combinations of Laplace eigenfunctions. As a resul…
The paper proves the existence of -invariant minimal hypersurfaces on certain Riemannian manifolds.
problem Existence of -invariant minimal hypersurfaces on specific Riemannian manifolds.
method Adapted Almgren-Pitts min-max theory to a -equivariant version.
result Existence of nontrivial closed smooth embedded -invariant minimal hypersurfaces.