The invention relates to materials which are stable at high temperatures and which have high specific surfaces. Said materials are produced by heating them to a temperature in a matrix above the later temperature at which they are used, e.g. aluminum oxide or zirconium oxide. The temperature of the specific surfaces thereof, after relatively long tempering, is 1100° C. or 1000° C., even above 50 m2/g or 10 m2/g. Carrier catalysts can be also be produced according to said method.