4 papers · 1 filter
The Weyl Law Meets Large-Scale Regularity on Ricci Shrinkers
Junrong Yan
We prove that the weighted Laplacian, or equivalently its conjugate Schrödinger operator, on every complete gradient Ricci shrinker satisfies the classical Weyl law. The main diffi…
A gluing formula for the -valued index of odd symmetric operators
Maxim Braverman, Ahmad Reza Haj Saeedi Sadegh, Junrong Yan
We investigate Dirac-type operator on involutive manifolds with boundary with symmetry, which forces the index of to vanish. We study the secondary -valued index of el…
Weyl Law for Schrödinger Operators on Noncompact Manifolds, Heat Kernel, and Karamata-Hardy-Littlewood Theorem
Xianzhe Dai, Junrong Yan
Building on our earlier work on heat kernel asymptotics for Schrödinger-type operators on noncompact manifolds, we establish both the classical and semiclassical Weyl laws for Schr…
Generalized Morse Functions, Excision and Higher Torsions
Martin Puchol, Junrong Yan
Comparing invariants from both topological and geometric perspectives is a key focus in index theorem. This paper compares higher analytic and topological torsions and establishes…