開放式課程>>自然科學學群>>幾何二>>第10講 Minimal Surface (cont.)

第10講 Minimal Surface (cont.)

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

 
L10_B
         1. Theorem: If x Is an Isothermal Parametrized Surface
              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
         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
         3. Proposition: Any Ruled Minimal Surface Is an Open
             Subset of a Plane 
or a Helicoid
         4. Theorem: There Is No Compact Minimal Surface 

 

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