Starts 4 Nov 2024 15:00
Ends 7 Nov 2024 17:00
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CIMPA-ICTP online course "Geometric Identities and their Applications on Rigidity Problems"
Hybrid
Leonardo Building - Luigi Stasi Seminar Room
For those wishing to participate online, please register here:
https://zoom.us/meeting/register/tJEtdO6qqT0tEtHQErKGnirdPRB3EACe8oQK#/registration
In person: ICTP Stasi Lecture Room
Date and Time:
Nov 4, 2024 03:00 PM
Nov 5, 2024 03:00 PM
Nov 6, 2024 03:00 PM
Nov 7, 2024 03:00 PM
Abstract: In recent years, Riemannian metrics that satisfy specific systems of partial differential equations involving a function (and/or a vector field) defined in the manifold have been extensively studied. Examples include geometric structures related to the class of static metrics that appear in General Relativity, such as the critical metrics of the volume functional. A powerful tool in this field is using integral identities (such as Reilly and Pohozaev-Schoen identities), which permit relate differential and geometric operators in Riemannian manifolds. One notable example is the proof by Reilly-Ros of Alexandrov's theorem via integral inequalities, where a crucial step is the Heintze-Karcher inequality, an inequality that follows directly from Reilly's identity and further indicates rigidity to the Euclidean ball in the case of equality. On the other hand, the Pohozaev-Schoen identity can be used to obtain area limitations for the boundary of static manifolds and to conclude rigidity from the known models.
https://zoom.us/meeting/register/tJEtdO6qqT0tEtHQErKGnirdPRB3EACe8oQK#/registration
In person: ICTP Stasi Lecture Room
Date and Time:
Nov 4, 2024 03:00 PM
Nov 5, 2024 03:00 PM
Nov 6, 2024 03:00 PM
Nov 7, 2024 03:00 PM
Abstract: In recent years, Riemannian metrics that satisfy specific systems of partial differential equations involving a function (and/or a vector field) defined in the manifold have been extensively studied. Examples include geometric structures related to the class of static metrics that appear in General Relativity, such as the critical metrics of the volume functional. A powerful tool in this field is using integral identities (such as Reilly and Pohozaev-Schoen identities), which permit relate differential and geometric operators in Riemannian manifolds. One notable example is the proof by Reilly-Ros of Alexandrov's theorem via integral inequalities, where a crucial step is the Heintze-Karcher inequality, an inequality that follows directly from Reilly's identity and further indicates rigidity to the Euclidean ball in the case of equality. On the other hand, the Pohozaev-Schoen identity can be used to obtain area limitations for the boundary of static manifolds and to conclude rigidity from the known models.
- Please note that the CIMPA/ICTP online courses will be recorded and broadcasted at ICTP.
- CIMPA does not provide certificates of attendance for online courses.
- CIMPA does not provide certificates of attendance for online courses.