Is it possible to install backer-board on a curved surface?
I have used HardieBacker, Wonderboard and Durock and I'd use 1/4 Wonderboard in this application. IIRC, it is the most ductile (bends before it breaks) of the three. On a stair subject to being kicked, you may want to use two sheets of quarter inch (the same trick for bending drywall) with troweled mortar between them. Basically, backerboard easily lets you fake a "dry pack" mortar bed:


  Traditionally, for wet applications, the arguably proper method is a "dry pack" mortar bed sloped to a tile drain followed by a hot-mop asphalt application, followed by floated cement followed by tile set in thin-set mortar. It is a method that is quite labor intensive involving specific steps. This is still a common method for commercial and residential applications, but becoming less so with the advent of modern alternative materials and techniques. –  Jimmy Fix-it


The 'tar' waterproofing is accomplished by the application of an anti-water membrane over your backerboard; embedding fiber tape along any seams or cracks. 

Even if one or both of the sandwiched backerboards does crack as you install it; the mortar will fill and set it back into a solid piece... hopefully. If the framing is sound, using screwed-down mortared-in-place backerboard and a liquid applied membrane will go a long way towards achieving a professional tile job. 

This is all assuming you have a nice, gently curved plywood substrate that you can screw to every 6~8" and not just 16"oc studs.



Ditra mat is possibly what you could use but I never have, and therefore cannot attest to it's functionality nor whether it is applicable, vertically: (emctiles.co.uk)