2024/02/17 by Yong-Geun Oh, Yong‐Geun Oh, Seungook Yu
Materials Science · Mathematics · #Gas Dynamics and Kinetic Theory #Spectral Theory in Mathematical Physics #Thermal properties of materials
paper · doi:10.1142/s0129167x24500198
openalex publication_date 2024/02/17 · openalex created_date 2024/02/18 · openalex updated_date 2026/07/28
In this paper, we establish nonlinear ellipticity of the equation of contact instantons with Legendrian boundary condition on punctured Riemann surfaces by proving the a priori elliptic coercive estimates for the contact instantons with Legendrian boundary condition, and prove an asymptotic exponential [Formula: see text]-convergence result at a puncture under the uniform [Formula: see text] bound. We prove that the asymptotic charge of contact instantons at the punctures under the Legendrian boundary condition vanishes. This eliminates the phenomenon of the appearance of spiraling cusp instanton along a Reeb core, which removes the only remaining obstacle towards the compactification and the Fredholm theory of the moduli space of contact instantons in the open string case, which plagues the closed string case. Leaving the study of [Formula: see text]-estimates and details of Gromov-Floer-Hofer style compactification of contact instantons to [ 27 ], we also derive an index formula which computes the virtual dimension of the moduli space. These results are the analytic basis for the sequels [ 27 – 29 ] and [ 36 ] containing applications to contact topology and contact Hamiltonian dynamics.