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The surface of shallow Ga[Al]As heterostructures is locally oxidized with an atomic force microscope. The electron gas underneath the oxide is depleted. We demonstrate experimentally that these depleted regions of the two-dimensional electron gas can be made highly resistive at liquid nitrogen temperatures. Thus, local anodic oxidation of high electron mobility transistors with an atomic force microscope provides a novel method to define nanostructures and in-plane gates. Two examples, namely antidots and quantum point contacts as in-plane gate transistors have been fabricated and their performance at low temperatures is discussed. © 1998 American Institute of Physics.