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401-5004-21L DR D-MATH

Prescribing Scalar Curvature in Conformal Geometry

Lecturers: Prof. Dr. Andrea Malchiodi
VVZ CR n/a

Last Updated: 2026-02-05 15:54:12

Abstract

Nachdiplom lecture

Content

We will consider the classical problem, proposed by Kazdan and Warner in the 70’s, of prescribing the scalar curvature of a Riemannian manifold via conformal deformations of the metric. This amounts to solving an elliptic nonlinear PDE with critical exponent, presenting difficulties due to lack of compactness. There are in general obstructions, but still several contributions to the existence theory have been given using different tehniques. These include Direct Methods of the Calculus of Variations, blow-​up analysis, Liouville theorems, gluing constructions and topological or Morse-​theoretical tools. We will give a general presentation of the subject, describing the principal contributions in the literature and arriving to more recent developments.

General Information

Language
English
Levels
DR

Examination

Type
no performance assessment

Course Components

Type Title Time & Place Hours
lecture Prescribing Scalar Curvature in Conformal Geometry
Time: 10:15 – 12:00
  • Tue 10:15-12:00 (HG G 43)
  • 26.03 Date 10:15-12:00 (HG G 43)
2 h weekly

Offered In

  • Doctoral Department of Mathematics (More Information at: The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM. WARNING: Do not mistake ECTS credits for credit points for doctoral studies!)