L10_A
1. Proof: A Parametrized Surface Is Minimal if and only
if A’(0)=0
2. Isothermal Parametrized Surface
3. Theorem: If x Is an Isothermal Parametrized Surface
Then x_uu＋x_vv=2(a^2)HN
Then x_uu＋x_vv=2(a^2)HN
L10_B
1. Theorem: If x Is an Isothermal Parametrized Surface
Then x_uu＋x_vv=2(a^2)HN (cont.)
Then x_uu＋x_vv=2(a^2)HN (cont.)
2. Harmonic Function
3. Corollary: An Isothermal Parametrized Surface Is
Minimal if and only if Its Coordinate Functions Are
Harmonic
Minimal if and only if Its Coordinate Functions Are
Harmonic
4. Introduction: Development of Minimal Surface
L10_C
1. Examples: Catenoid and Helicoid
2. Proposition: Any Minimal Surface of Revolution Is an
Open Subset of a Plane or a Catenoid
Open Subset of a Plane or a Catenoid
3. Proposition: Any Ruled Minimal Surface Is an Open
Subset of a Plane or a Helicoid
Subset of a Plane or a Helicoid
4. Theorem: There Is No Compact Minimal Surface
OCW _ Subtitle List (Geometry II).pdf
