We study a linear operator associated with a closed non-exact 1-form b defined on a smooth closed orientable surface M of genus g > 1. Here we present two proofs that reveal the interplay between the global solvability of the operator and the global topology of the surface. The first result brings an answer for the global solvability when the system is defined by a generic Morse 1-form. Necessary conditions for the global solvability bearing on the sublevel and superlevel sets of primitives of a smooth 1-form b have already been established; we also present a more intuitive proof of this result.

Adalberto Panobianco Bergamasco, Alberto Parmeggiani, Sergio Luis Zani, Giuliano Angelo Zugliani (2018). GEOMETRICAL PROOFS FOR THE GLOBAL SOLVABILITY OF SYSTEMS. MATHEMATISCHE NACHRICHTEN, 291(16), 2367-2380 [10.1002/mana.201700300].

GEOMETRICAL PROOFS FOR THE GLOBAL SOLVABILITY OF SYSTEMS

Alberto Parmeggiani;Giuliano Angelo Zugliani
2018

Abstract

We study a linear operator associated with a closed non-exact 1-form b defined on a smooth closed orientable surface M of genus g > 1. Here we present two proofs that reveal the interplay between the global solvability of the operator and the global topology of the surface. The first result brings an answer for the global solvability when the system is defined by a generic Morse 1-form. Necessary conditions for the global solvability bearing on the sublevel and superlevel sets of primitives of a smooth 1-form b have already been established; we also present a more intuitive proof of this result.
2018
Adalberto Panobianco Bergamasco, Alberto Parmeggiani, Sergio Luis Zani, Giuliano Angelo Zugliani (2018). GEOMETRICAL PROOFS FOR THE GLOBAL SOLVABILITY OF SYSTEMS. MATHEMATISCHE NACHRICHTEN, 291(16), 2367-2380 [10.1002/mana.201700300].
Adalberto Panobianco Bergamasco; Alberto Parmeggiani; Sergio Luis Zani; Giuliano Angelo Zugliani
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/649447
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact