One of the primary reasons why a frying pan may bow is that it has a thin base. When metal is heated it expands and becomes more pliable. With thin-based pans this process is more pronounced as they lack the rigidity inherent to heavy-based pans. As such, when heated, the metal warps.
Frying pans may warp if they are subjected to a rapid change in temperature, by being taken directly from a hot stove and immersed in or placed under running cold water. This causes the hot, expanded metal to contract too quickly, kinking or bowing in the process.
Sometimes the frying pan is heated to a temperature that it is simply not designed to withstand. Even if the warped pan is left to cool naturally, the bow may be permanent. Always read the directions that come with a new pan, as they may indicate the temperature range for which it is suitable.
Other than avoiding placing hot pans into cold water and heating pans to too high a temperature, the best way to prevent bowing a frying pan is to purchase a heavy-duty, thick-based version. The density and rigidity of heavy-based pans protects them from warping in all but the most extreme heat or changes of temperature.