Minicourse Part 3: F. Martín (U Granada)

10:30-12:05 Lectures 5 & 6 (Room: 04.4.01)
12:05- Lunch & coffees

A compact, graduate-level mini-course introducing self-translating solitons (“translators”) for the mean curvature flow: definition and basic geometric/PDE properties; the classical and newer families of examples; standard construction techniques (graphical methods, ODE reductions, Jenkins–Serrin type constructions, gluing/desingularization); key classification theorems in low dimensions; and the role of *collapsed vs. noncollapsed* translators as singularity models. The course mixes rigorous statements, sketch proofs, and short exercises so participants leave able to read current papers on translators.

 * Basic differential geometry of hypersurfaces (mean curvature, second fundamental form).

 * Familiarity with parabolic PDE intuition (maximum principle, curvature flow basics).

 * Some experience with elliptic PDE methods and geometric measure theory is helpful but not mandatory.

 * Know the definition of a self-translating soliton and its equivalent elliptic PDE.

 * Recognize and compute the geometry of the principal classical examples (grim reaper, bowl soliton, translating catenoids/tilted grim, helicoidal translators, Nguyen’s tridents, etc.). [1][2]

 * Understand at a high level the methods used to produce new examples (graphical Jenkins–Serrin, ODE reductions, gluing and limit procedures). [2][3]

 * Be aware of the major classification/convexity results in R³ and recent progress in higher dimensions. [4]

 * Understand the definition and geometric consequences of being collapsed vs noncollapsed, with examples and implications for singularity analysis. [5][6]