Carlotto--Schulz Numerical Data This page gives the numerical values of r0 and T/4 used to generate the Carlotto--Schulz minimal hypersurfaces.
Home Select a value of n:
n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 n = 8 n = 9 n = 10 n = 11 n = 12 n = 13 n = 14 n = 15 n = 16 n = 17 n = 18 n = 19 n = 20 n = 21 n = 22 n = 23 n = 24 n = 25 n = 26 n = 27 n = 28 n = 29 n = 30 n = 31 n = 32 n = 33 n = 34 n = 35 n = 36 n = 37 n = 38 n = 39 n = 40 n = 41 n = 42 n = 43 n = 44 n = 45 n = 46 n = 47 n = 48 n = 49 n = 50 n = 51 n = 52 n = 53 n = 54 n = 55 n = 56 n = 57 n = 58 n = 59 n = 60 n = 61 n = 62 n = 63 n = 64 n = 65 n = 66 n = 67 n = 68 n = 69 n = 70 n = 71 n = 72 n = 73 n = 74 n = 75 n = 76 n = 77 n = 78 n = 79 n = 80 n = 81 n = 82 n = 83 n = 84 n = 85 n = 86 n = 87 n = 88 n = 89 n = 90 n = 91 n = 92 n = 93 n = 94 n = 95 n = 96 n = 97 n = 98 n = 99 n = 100 n = 101 n = 102 n = 103 n = 104 n = 105 n = 106 n = 107 n = 108 n = 109 n = 110 n = 111 n = 112 n = 113 n = 114 n = 115 n = 116 n = 117 n = 118 n = 119 n = 120 n = 121 n = 122 n = 123 n = 124 n = 125 n = 126 n = 127 n = 128 n = 129 n = 130 n = 131 n = 132 n = 133 n = 134 n = 135 n = 136 n = 137 n = 138 n = 139 n = 140 n = 141 n = 142 n = 143 n = 144 n = 145 n = 146 n = 147 n = 148 n = 149 n = 150 n = 151 n = 152 n = 153 n = 154 n = 155 n = 156 n = 157 n = 158 n = 159 n = 160 n = 161 n = 162 n = 163 n = 164 n = 165 n = 166 n = 167 n = 168 n = 169 n = 170 n = 171 n = 172 n = 173 n = 174 n = 175 n = 176 n = 177 n = 178 n = 179 n = 180 n = 181 n = 182 n = 183 n = 184 n = 185 n = 186 n = 187 n = 188 n = 189 n = 190 n = 191 n = 192 n = 193 n = 194 n = 195 n = 196 n = 197 n = 198 n = 199 n = 200 n = 201 n = 202 n = 203 n = 204 n = 205 n = 206 n = 207 n = 208 n = 209 n = 210 n = 211 n = 212 n = 213 n = 214 n = 215 n = 216 n = 217 n = 218 n = 219 n = 220 n = 221 n = 222 n = 223 n = 224 n = 225 n = 226 n = 227 n = 228 n = 229 n = 230 n = 231 n = 232 n = 233 n = 234 n = 235 n = 236 n = 237 n = 238 n = 239 n = 240 n = 241 n = 242 n = 243 n = 244 n = 245 n = 246 n = 247 n = 248 n = 249 n = 250 n = 251 n = 252 n = 253 n = 254 n = 255 n = 256 n = 257 n = 258 n = 259 n = 260 Values n: 2
r0 : 1.232150187248573
T/4: 0.7280351818767343
What do these numbers represent? For each integer n > 1, Carlotto and Schulz proved that there exist numbers r0 in (0, π) and s* = T/4 such that the solution (r(t), θ(t), α(t)) of the differential equation system that produces embedded minimal hypersurfaces in the 2n-dimensional sphere, with initial conditions
θ(0) = π/4, r(0) = r0 , α(0) = −π/2
satisfies
θ(s*) > 0, r(s*) = π/2, α(s*) = 0.
The values displayed above are numerical approximations of r0 and T/4 for the corresponding value of n.