15 citations · 25 across the 12 of their papers we have counts for
12 papers
Liouville regular Jordan curves
Tomohiro Asano, Yuichi Ike
We investigate the class of Liouville regular Jordan curves, which was introduced in our previous paper under the phrase "Jordan curves that admit continuous Legendrian lifts". We…
Topological constraints on clean Lagrangian intersections via microlocal sheaf theory
Tomohiro Asano, Yukihiro Okamoto
Fix a knot in and consider a Lagrangian submanifold of that is isotopic to the conormal bundle of by a compactly supported Hamilton…
-rigidity of Legendrians and coisotropics via sheaf quantization
Tomohiro Asano, Yuichi Ike, Christopher Kuo +1
We prove that in the standard cosphere bundle, for any contact homeomorphism in the closure of the compactly supported contactomorphism group, when the image of a coisotropic subma…
The rectifiable rectangular peg problem
Tomohiro Asano, Yuichi Ike
We give an affirmative answer to the rectangular peg problem for a large class of continuous Jordan curves that contains all rectifiable curves and Stromquist's locally monotone cu…
Regular Lagrangians are smooth Lagrangians
Tomohiro Asano, Stéphane Guillermou, Yuichi Ike +1
We prove that for any element in the -completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its -support is a smooth Lagrangian su…
Heavy subsets from microsupports
Tomohiro Asano
We construct partial symplectic quasi-states on a cotangent bundle with the use of microlocal sheaf theory. We also give criteria and characterization for heaviness/superheaviness…
Lagrangian cobordism and shadow distance in Tamarkin category
Tomohiro Asano, Yuichi Ike, Wenyuan Li
We study exact Lagrangian cobordisms between exact Lagrangians in a cotangent bundle in the sense of Arnol'd, using microlocal theory of sheaves. We construct a sheaf quantization…
A note on Hamiltonian stability for sheaves
Tomohiro Asano, Yuichi Ike
We show a strong Hamiltonian stability result for a simpler and larger distance on the Tamarkin category. We also give a stability result with support conditions.
The -support as a micro-support
Tomohiro Asano, Stéphane Guillermou, Vincent Humilière +2
We prove that for any element in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the -…
Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
Tomohiro Asano, Yuichi Ike
We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleavin…
Sheaf quantization and intersection of rational Lagrangian immersions
Tomohiro Asano, Yuichi Ike
We study rational Lagrangian immersions in a cotangent bundle, based on the microlocal theory of sheaves. We construct a sheaf quantization of a rational Lagrangian immersion and i…
Persistence-like distance on Tamarkin's category and symplectic displacement energy
Tomohiro Asano, Yuichi Ike
We introduce a persistence-like pseudo-distance on Tamarkin's category and prove that the distance between an object and its Hamiltonian deformation is at most the Hofer norm of th…