Hot spots conjecture (3D)

About this app

An insulated plate is heated: where does the hottest point end up? The first Neumann eigenfunction as relief and heat map for a disc, ellipse, stadium, bean, star, a shape with a hole or your own drawing. Without holes the maximum and minimum lie on the boundary and there is no interior critical point (preprint openai/math, family 369). Heat flow with a track of the hot spot, eigenspace mix for a double eigenvalue.

Subject: Open problems, solved by AI

More from Open problems, solved by AI

• The plane is not five-colourable (Hadwiger–Nelson)
• Triangular billiards — irrational angles mix (3D)
• Triangular lattice — universal optimality
• Gaussian moat — no path to infinity
• Isoperimetry in the cubic torus (3D)
• Crossing numbers — Turán's brickyard
• Standard map: chaos on genuine area

A VisuApp by heyprof: interactive, free in your browser, no sign-up. What is a VisuApp? · All apps